f 


REESE   LIBRARY 


UNIVERSITY  OF  CALIFORNIA 

^ecerceJ         £/6^  ,'il 

•  ''h'l  V.V  S 10 1 1 N  .  V( ) .   ^  Q   /  f  *f. 


> 


;;  '   '-ft 

m  M 


1 


i  .:  "       -  ffl  • 

: 


.-•    • 


AN    OUTLINE 


OF 


THE  THEORY  OF  SOLUTION 

AND    ITS    RESULTS. 
FOR    CHEMISTS    AND    ELECTRICIANS. 


BY 


J.  LIVINGSTON  R.   MORGAN,  PH.D.  'LEIPZIG,) 

Instructor  in  Quantitative  A  nalysis, 
Polytechnic  Institute,  Brooklyn. 


FIRST   EDITION. 
FIRST    THOUSAND. 


f  OFTHE  ^       >. 

(UNIVERSITY) 

\^  op  ^/ 


NEW   YORK: 

JOHN     WILEY    &    SONS. 

LONDON  :   CHAPMAN  &  HALL,   LIMITED. 

1897. 


Copyright,  1897, 

BY 

J.  L.  R.  MORGAN 


ROBERT  DRUMMOND,   ELECTROTYPER  AND  PRINTER,  J<BVf  YORK. 


TO 

professor  JBr,  S^ilijrlm  ©sttoalto, 

OF    THE    UNIVERSITY    OK    LEIPZIG, 
THIS    LITTLE    BOOK    IS    RESPECTFULLY 

DEDICATED 

AS    A    SMALL    TOKEN    OF 

GRATITUDE   AND  ESTEEM 

BY 

THE   AUTHOR. 


OF  THE 

UNIVERSITY 


PREFACE. 


A  KNOWLEDGE  of  the  Theory  of  Solution  and  its 
results  is  so  important,  to  workers  in  all  branches  of 
chemistry  and  electricity,  that  the  following  pages 
have  been  compiled,  containing  an  elementary  treat- 
ment of  the  subject,  which  is  advanced  enough  to 
enable  the  reader  to  follow  the  work  which  is  being 
done  to-day.  The  essence  of  them  is  to  be  given  in 
a  course  of  four  lectures,  by  the  author,  before  the 
Brooklyn  Institute  of  Arts  and  Sciences  in  March. 
The  mathematical  part  has  been  omitted  as  much  as 
possible,  but  references  are  given.  If  by  this  sketch 
the  author  can  induce  any  one  to  go  deeper  into  the 
subject,  he  will  feel  more  than  repaid  for  his  work. 
To  any  such,  the  following  books  are  very  highly 
recommended: 

Ostwald :  Lehrbuch  der  allgemeinen  Chemie.  2 
vols.  Leipzig  (1892-7). 

Ostwald:  Scientific  Aspects  of  Analytical  Chem- 
istry. Trans,  by  McGowan.  Macmillan,  1896. 

Le  Blanc  :  Lehrbuch  der  Elektrochemie.  Leipzig, 
1896. 

J.  L.  R.  M. 

POLYTECHNIC  INSTITUTE, 

BROOKLYN,  January,  1897. 


CONTENTS. 


CHAPTER  I. 

PAGE 

THE  THEORY  OF  SOLUTION. 

The  Gas  Laws i 

Abnormal- Results  with  Gases 5 

Solution 8 

Electrolytic  Dissociation 16 

CHAPTER  II. 

METHODS   FOR  THE  DETERMINATION  OF   ELECTROLYTIC  DIS- 
SOCIATION     27 

CHAPTER  III. 

THE  THEORY  OF  THE  VOLTAIC  CELL 36 

Dissociation  by  Aid  of  E.  M.  F 47 

Practical  Primary  and  Secondary  Batteries 49 

CHAPTER  IV. 

ANALYTICAL  CHEMISTRY  FROM  STANDPOINT  OF  ELECTROLYTIC 

DISSOCIATION 56 

Indicators    for  Volumetric  Analysis  and  the  Theory  of 

their  Action 62 

vii 


AN  OUTLINE  OF  THE  THEORY  OF 
SOLUTION  AND  ITS  RESULTS 


CHAPTER    I. 
THE  THEORY   OF   SOLUTION. 

THE  GAS  LAWS. 

IN  order  to  understand  the  rise  of  the  Theory  of 
Solution,  it  will  be  necessary  for  us  to  review,  in  brief, 
the  laws  for  the  behavior  of  gases  during  the  different 
changes  of  condition  which  they  may  undergo.  First 
we  will  turn  to  the  Lazv  of  Mariotte ;  it  may  be  ex- 
pressed as  follows:  The  temperature  remaining  the 
same,  the  volume  of  a  given  quantity  of  gas  is  inversely 
proportional  to  the  pressure  to  which  it  is  exposed. 
That  is, 

P'  :/>::  V\  V1 ', 

where  V  and  V  represent  respectively  the  volumes 
before  and  after  the  pressure  is  changed  from  P  to  P' . 
Volumes  of  gases  are  measured  in  cubic  centimeters 
at  a  certain  temperature  and  pressure,  while  pressures 


2  THE    THEORY  OF  SOLUTION. 

are  measured  in  millimeters  of  mercury  (in  a  barom- 
eter). The  Law  of  Charles  is:  The  pressure  remaining 
the  same,  tJie  volume  of  a  given  quantity  of  a  gas  is 
directly  proportional  to  its  absolute  temperature.  It 
has  been  found  that  a  gas  expands  (contracts)  1/273 
of  its  volume,  at  o°  centigrade  (C.),  for  every  increase 
(decrease)  in  temperature  of  i°  C. ;  hence,  if  a  volume 
of  gas,  at  o°  C.,  should  have  its  temperature  lowered 
through  273°,  the  contraction  would  equal  the  volume. 
This  point  (273°  below  o°  C.)  is  called  the  absolute 
zero,  and  temperatures  reckoned  from  this  point 
absolute  temperatures.  The  proportion  then  for  this 
law 

T :  T'  ::  V :  V 

where  T  is  equal  to  the  centigrade  temperature  -|- 
273°,  and  V  is  as  before.  The  Law  of  Dalton  is  best 
expressed,  perhaps,  in  the  following  form:  The  pres- 
sure exerted  upon  the  walls  of  a  vessel,  containing  a  mix- 
ture of  gases,  is  equal  to  the  sum  of  the  pressures  which 
the  single  gases  would  exert,  were  they  alone  in  the 
vessel.  The  law  of  Avogadro  is  of  paramount  impor- 
tance. According  to  it:  All  gases,  under  the  same  con- 
ditions of  pressure  and  temperature,  contain  in  unit 
volume  the  same  number  of  molecules.  The  law  of 
Mariotte  is  generally  written,  when  the  temperature 
does  not  vary, 

pv  =  constant, 

for  we  know  that  /  and  v  are  inversely  proportional, 
and  hence  when  one  increases  the  other  decreases  by 


THE    THEORY  OF  SOLUTION.  3 

the  same  amount,  and  consequently  the  product 
remains  constant. 

The  law  of  Mariotte  and  that  of  Charles  are  usually 
united  in  a  form  which  gives  the  state  of  the  gas 
under  all  conditions.  If,  for  example,  we  have  a  gas 
at  a  certain  volume  at  o°  and  760  mm.  pressure  and 
keep  the  pressure  constant,  allowing  the  temperature 
to  vary,  the  volume  becomes 

v  =  v.(i  +  at). 

If  now,  instead  of  keeping  the  pressure  constant,  we 
vary  it  and  keep  the  volume  constant,  then  the  pres- 
sure must  increase  just  as  the  volume  did  before. 
That  is, 

/=A(i  +  "0- 

The  v0  and  /•„  refer  to  the  standard  state  (o°  and  760 
mm.  pressure).  By  uniting  these  two  we  obtain 


t); 

^ 


j>v  =  j>9v.(i  +  at 
but 

/=  r-273 

and  (a  ==  ^fa)  hence 


273 


4  THE    THEORY  OF  SOLUTION. 

1)  i) 

As   will   be  seen,   this  term  — °  is  a  constan        The 

273 

letter  R  is  usually  substituted  for  it,  so  that  we  have, 
as  the  equation  of  state  of  a  perfect  gas, 

fv  =  RT\ 

or,  since  R  is  found,   by  calculation,  to  be  equal  to 
84700  centimeter-grams,* 

pv  =  84700  T. 

This  R,  which    refers    to    only  one    mol    (molecular 
weight  in  grams)  of  gas,  is  called  the  gas  constant. 

According  to  Avogadro's  law,  equal  volumes  of  all 
gases  contain  the  same  number  of  molecules.  This 
gives  us  a  method  of  determining  the  molecular  weight 
of  substances  in  gas  form,  which  has  been  used  very 
largely.  By  Avogadro's  law, 

m.       m~       mH 

-~  —  -  *  =  -T-  —  constant, 

at       a*       aH 

where  ;«,,  ;«, ,  mn  ,  are  molecular  weights,  and  d^ ,  d^ , 
dn  are  the  densities  of  the  corresponding  gases.      If 

*  As  calculated  for  one  mol  of  oxygen,  but  it  is  the  same  for 
one  mol  of  any  other  gas.  z/0(i  gr.  O  at  76  cms.  pressure  and 
o°  C.)  =  699.25  c.c.,  /0  =  76  cms.  of  a  column  of  mercury  i  cm. 
in  diameter.  Sp.  gr.  of  Hg  =  13.5.  Hence  the  weight  of  the 
column  =  76  X  13.5  =  1033.2  grms.,  T—  273° 


Therefore      ~  for  32  grams  (mol)  = 


32  X  =  8468S  cm.  grmji> 

(84700  in  round  numbers),  i.e. ,  equal  to  an  energy  whit  h  would  lift 
84700  grms.  i  cm.  in  I  second. 


THE    THEORY  OF  SOLUTION.  5 

we  now  take  hydrogen  as  unity,  with  respect  to  atomic 
weight  and  density,'  then  mt  (H)  will  equal  2  (two 
atoms  to  one  molecule),  dl  =  I,  and  any  other  molec- 
ular weight,  m^  ,  can  be  found  by  solving  the  equation 


m 


hence 


That  is,  the  molecular  weight  of  any  substay.ce  is  equal 
to  twice  its  density  in  gas  form,  hydrogen  being  unity. 

So  much  for  the  laws  of  gases.  I  have  given  them 
in  this  short  and  concise  form,  for  we  will  have  to  refer 
to  them  very  often,  and  they  are  all  necessary,  for,  as 
we  will  find,  they  are  also,  with  a  few  modifications, 
the  laws  for  solution  The  dissolved  substance  acts  in 
its  solution  just  as  a  gas  would  when  shut  into  a  cer- 
tain volume,  the  volume  of  the  solvent  being  the  vol- 
ume, and  the  substance  itself  as  the  gas.  The  term 
which  is  equivalent  to  pressure  will  be  developed  later. 

ABNORMAL  RESULTS  WITH  GASES. 

The  laws  for  gases,  given  in  the  last  section,  do  not 
hold  strictly  for  all  gases,  but  do  (fairly)  for  all  per- 
fect ones.  The  vapors  of  many  substances,  however, 
were  found  to  give  very  strange  results;  and  upon 
these  we  will  dwell  in  this  section.  Thus,  long  ago, 
it  was  found  that  the  vapor  of  ammonium  chloride 
gave  a  density  which  was  but  one  half  what  it  should 
be,  according  to  its  accepted  molecular  weight.  There 
are  but  two  ways  of  explaining  this  abnormal  action, 


0  THE    THEORY  OF  SOLUTION. 

viz. :  either  Avogadro's  law  does  not  hold  good,  or  the 
substance  is  decomposed  by  the  heat  into  its  constit- 
uents, according  to  the  equation 

NH4Clti;NH,+  HC1. 

The  sign  ^  meaning  that  the  reaction  goes  forward  or 
backward,  according  as  the  temperature  is  high  or  low. 
Avogadro's  law,  however,  holds  for  all  other  sub- 
stances, so  that  it  was  concluded  at  the  time  that  the 
latter  reason  was  the  true  one,  and  somewhat  later  it 
was  proven  conclusively  to  be  so.  This  process  is 
called  dissociation. 

Of  course  if  the  vapor  density  is  just  one  half  what 
it  should  be,  then  the  substance  must  be  completely 
dissociated,  according  to  the  above  reaction;  i.e.,  for 
every  molecule  present  before  the  process,  we  have  two 
after.  Then  since  the  number  of  molecules  is  twice 
as  large,  if  we  start  with  one  volume  of  NH4C1  gas,  we 
will  have  two  volumes  of  the  mixed  gases  under  the 
same  conditions.  These  two  volumes,  however,  weigh 
the  same  as  the  original  one  volume;  and  conse- 
quently one  volume  would  weigh  but  one  half  what 
it  should;  i.e.,  the  vapor  density  is  one  half  the 
normal.  These  results  were  found  to  depend  on  the 
temperature,  i  e.,  the  higher  the  temperature  the 
smaller  (down  to  a  certain  limit)  the  vapor  density. 

The  method  by  which  this  dissociation  was  proven 
depended  upon  the  unequal  velocity  of  diffusion  of  NH3 
and  HC1  gas  through  a  porous  plate.  In  this  way 
the  two  free  gases  were  separated,  the  undecomposed 
NH4C1  gas  not  interfering  with  them. 


THE   THEORY  OF  SOLUTION.  J 

The  simplest  way  of  studying  the  laws  governing 
this  dissociation  is  to  inclose  a  solid,  which  decom- 
poses by  heat  into  two  gases,  in  a  vessel  provided 
with  a  source  of  heat,  a  pressure-gauge,  and  a  ther- 
mometer. If  we  now  raise  the  temperature  the  solid 
volatilizes,  and  the  NH4C1  gas  dissociates  until  the 
NH4C1,  the  NH8 ,  and  the  HC1  gases  reach  a  certain 
pressure  (corresponding  to  the  certain  temperature) 
when  it  ceases.  If  now,  after  equilibrium  is  estab- 
lished, we  open  the  stop-cock,  some  of  the  gas  es- 
capes and  the  pressure  falls,  it  rises  again,  however, 
as  soon  as  the  cock  is  closed,  and  continues  to  rise 
until  that  same  pressure  is  reached  which  existed 
before  at' that  temperature.  Let  us  now  consider,  for 
the  sake  of  simplicity,  a  case  where  the  solid  NH4C1  is 
dissociated  completely  into  NH3  and  HC1  gas.  This 
will  act  just  as  the  other  if  we  open  the  cock.  We 
will-  now,  however,  imagine  NHS  gas  forced  into  the 
vessel,  and  will  see  what  will  happen.  We  observe 
no  change  in  the  pressure,  but  only  that  solid  NH4C1  is 
formed;  that  is,  the  pressure  of  the  ammonia  becomes 
so  great  that  it  condenses  its  form,  and  in  so  doing 
unites  again  with  the  HC1  forming  NH4C1.  This 
process  continues  until  all  the  HC1  is  used  up,  and 
then  the  condition  is  altered,  for  one  of  the  constit- 
uents in  the  equilibrium  disappears,  and  then,  and 
then  only,  does  the  pressure  rise.  In  this  latter  case, 
after  all  the  HC1  is  used  up,  we  are  simply  compress- 
ing the  NH3  gas. 

All  this  can  be  proven  experimentally,  and  we 
always  find  that  if  we  add  an  amount  of  one  of  the 
products  of  dissociation,  the  dissociation  goes  backivard 


8  THE    THEORY  OF  SOLUTION. 

in  a  corresponding  degree,  and  the  pressure  remains  con- 
stant. Addition  of  an  indifferent  gas,  except  that  it 
increases  the  total  pressure  according  to  Dalton's  laws, 
has  no  effect, 

The  equilibrium  which  is  reached  after  a  certain 
time  is  not  necessarily  a  state  of  absolute  rest,  but 
rather  a  case  of  where  the  amount  of  NH4C1  formed, 
in  unit  of  time,  is  the  same  as  that  decomposed.  It 
is  then  a  simple  exchange  of  matter,  the  total  amount 
of  the  gas  remaining  the  same.* 

With  this  we  will  close  our  consideration  of  gases; 
but  it  will  be  well  to  understand  their  behavior  thor- 
oughly before  proceeding  farther,  for  the  behavior  of 
substances  in  solution  is  exactly  analogous. 

To  explain  our  abnormal  results  it  has  been  assumed 
(and  proved)  necessary  to  consider  them  as  dissociated 
into  smaller  particles,  and  even  this  we  will  find  to  be 
true  also  for  solutions. 

SOLUTION. 

If  in  a  tall  jar  we  place  a  layer  of  pure  water  over 
a  solution  of  sugar,  being  careful  not  to  mix  them,  the 
sugar  molecules  immediately  begin  to  diffuse  through 
the  water,  and  only  cease  when  the  solution  through- 
out is  homogeneous,  i.e.,  of  the  same  concentration. 
Let  us  now  suppose,  in  this  experiment,  a  semi- 
permeable  partition  (which  allows  passage  to  the 
water  molecules,  but  not  to  those  of  sugar)  to  be 


*  It  may  be  well  to  mention  here  that  all  cases  of  equilibrium 
are  considered  in  this  way. 


THE    THEORY  OF  SOLUTION'.  9 

placed  between  the  water  and  the  solution.  Imme- 
diately a  pressure  is  exerted  upon  the  partition  which 
has  for  its  cause,  just  as  with  gases,  the  tendency  of 
the  molecules  to  get  out  of  the  space  in  which  they 
are  inclosed.  Here  the  sugar  molecules  are  striving 
to  wander  to  the  water,  but  are  prevented  by  the 
partition;  and  consequently  they  exert  a  pressure 
upon  it  which  is  equal  to  the  sum  of  those  of  the 
single  sugar  molecules.  By  a  contrivance  for  utilizing 
this  pressure  (if  one  could  be  found),  we  could  run  an 
engine,  just  as  we  do  now  with  gas  by  its  pressure 
upon  a  piston.  The  first  pressure,  as  will  be  seen 
later,  can  be  calculated  in  the  same  manner  as  the 
second. 

This  pressure  in  solutions  has  been  measured  by 
Prof.  Pfeffer  (and  others),  and  called  by  him  Osmotic 
Pressure.  The  great  objection  to  his  method  is  the 
difficulty  experienced  in  preparing  the  semi-permeable 
partition ;  still  Pfeffer  has  succeeded  in  making  very 
good  ones  from  copper  ferrocyanide  and  other  sub- 
stances.* His  apparatus  consists  of  a  porous  cell 
which  he  coats  with  the  semi-permeable  film  and  fills 
with  the  solution  to  be  used;  this  is  then  connected 
tightly  with  a  long  tube  containing  mercury,  by  which 
the  pressure  is  measured.  To  make  a  determination 
he  places  the  cell  in  a  jar  of  water  and,  after  allowing 
it  to  stand,  notes  the  height  of  the  mercury  in  the 
tube;  this  gives  the  desired  pressure. 

These  osmotic  pressures  are  enormous,  as  may  be 


*  See  Pfeffer,  Osmotische  Untersuchungen  (Leipzig,  1887),  for 
apparatus  and  results. 


OF  THE 


UNIVERSITY; 


10  THE    THEORY  OF  SOLUTION. 

seen  by  a  glance  at  the  following  table  from  Pfeffer.* 
Under  c  is  the  percentage  of  sugar  in  the  solution, 
and  under  p  the  pressure  resulting  in  centimeters  of 
mercury. 

Sugar  Solution. 

'(ft  /(cm.)  t 

c 

I  53.8  53.8 

I  53.2  53.2 

2  101.6  50.8 

2.74  151.8  55.4    ' 

4  208.2  52.1 

6  307-5  5i-3 

i  53-5  53-5 

The  last  column,  -,  contains  the  ratio  of  osmotic 
c 

pressure  to  concentration  of  sugar.  Considering  the 
size  of  the  possible  experimental  error,  it  remains  quite 
constant;  thus  proving  that  osmotic  pressure  is  propor- 
tional to  the  concentration  of  substance  in  tJie  solution. 
The  higher  pressures  seem  to  be  slightly  too  small, 

P 
thus  making  -  too  small;  this  is  explained  by  the  fact 

that,  for  such  high  pressures,  the  film  is  not  entirely 
impassable  for  sugar  molecules,  and  so  a  few  go 
through,  thus  causing  a  loss  of  pressure. 

It  has  been  found  that  osmotic  pressure  is  also  pro- 
portional to  the  absolute  temperature  (i.e.,  °  C.  -|-  273°). 
These  laws  have  been  found  to  be  true  not  only  for 


1.  c. 


THE    THEORY  OF  SOLUTION.  II 

sugar,  but  for  all  substances  which  do  not  conduct 
(or  conduct  very  slightly)  the  electric  current. 
•  We  must  remember  here  that  the  partition  is  not 
the  cause  of  the  pressure,  but  simply  the  condition 
necessary  to  make  it  visible  and  determinable.  The 
cell  acts  as  if  there  is  a  partial  vacuum  in  it  for 
water,  and  this  flows  inside,  and  continues  to  flow, 
if  not  prevented,  until  the  concentration  in  the  cell 
and  out  of  it  is  the  same.  This  pressure  becomes 
smaller  as  the  difference  of  concentration  does. 
There  is  a  tendency  always  to  reduce  the  difference  of 
concentration,  i.e.,  the  pressure,  of  the  two  liquids, 
just  as  there  is  with  gases.  The  pressure,  in  our  ex- 
ample, of  the  sugar  molecules  to  get  to  the  water  is 
the  same  as  that  of  the  water  to  get  to  the  sugar.  It 
is  thus  a  mutual  affinity,  and  so  we  would  expect  to 
get  different  pressures  for  different  solvents  (which  we 
do).  If  then  the  sugar  molecules  cannot  get  out  of 
the  cell,  the  water  goes  in,  and  thus  exerts  the  same 
pressure  inward  as  the  sugar  does  outwards.  The 
water  not  being  able  to  go  in,  in  our  experiment,  the 
mercury  is  raised  to  a  height  corresponding  to  the 
pressure. 

These  enormous  pressures  appear,  at  first  glance,  to 
be  impossible,  for  it  does  not  seem  possible  that  any 
substance  could  resist  them.  But  when  we  remember 
that  our  vessels  have  not  semi-permeable  walls,  and 
so  the  pressure  is  not  exerted  upon  them,  the  diffi- 
culty of  belief  is  removed.  If  they  had  such  walls, 
they  could  not  resist,  but  would  burst  immediately, 
as  do  plant-cells  (containing  concentrated  solution) 
when  placed  in  water. 


12  THE    THEORY  OF  SOLUTION. 

Let  us  now  recall,  for  a  moment,  the  equation  of 
state,  for  gases;  it  is 

pv  =  RT.         (R  =  84700  cm.gms.). 

We  have  found  that  —  is  a  constant   for  solutions. 

c 

This  is  the  same  as  pv  (where/  is  osmotic  pressure) 
for  -  =  v\  and  we  know  that  osmotic  pressure  is  pro- 

portional to  the  absolute  temperature.  Hence  we 
have,  for  solutions,  the  equation  of  state 

pv  —  R'T,         (R'  =  constant) 

which  is  of  the  same  form  as  the  one  for  gases.  We 
will  now  calculate  R'  and  see  if  it  has  any  relation  to 
R,  the  gas  constant.  We  must  remember,  however, 
that  R,  in  the  gas  equation,  was  calculated  for  one 
mol  of  gas;  so  in  this  case  we  will  also  consider  Rf  for 
one  mol  of  substance  in  solution.  This  was  first  done 
by  van't  HofT,  the  originator  of  the  Theory  of  Solu- 
tion. For  a  one  per  cent  solution  of  sugar  (o°  C.) 
Pfeffer  found  an  osmotic  pressure  of  49.3  cms.  of  mer- 
cury, which  is  equal  to  49.3  X  13.59  —  671  grams 
per  square  centimeter.  The  molecular  weight  of  sugar 
(C12HaaOn)  is  342;  the  volume  therefore,  in  which  one 
mol  is  dissolved  (i$  solution),  is  34200  c.c.,  and 
T  =  273  ;  hence 

/„?'.  671  X  ioo 

—  -.--  342  --      —      =  84200  cm.  grms.,* 


ioo  cc.  contain  i  gram. 


THE    THEORY   OF  SOLUTION.  1 3 

and  we  have  practically  the  same  constant  as  for  gases. 
In  the  same  way  van't  Hoff*  found  all  the  gas  laws 
to  hold  for  solutions,  when  by  v  we  understand  the 

dilution  (  — ),  and  by/  the  osmotic  pressure. 

This  astonishing  fact  is  the  basis  of  the  Theory  of 
Solution,  and  van't  Hoff  announced  it  as  follows: 

The  osmotic  pressure  of  a  substance  in  solution  is  the 
same  pressure  as  it  would  exert  were  it  in  gas  form, 
at  the  same  temperature  and  occupying  the  same  volume. 
In  other  words,  a  mol  of  any  substance  dissolved  in  a 
given  amount  of  water  exerts  the  same  osmotic  pres- 
sure, at  the  same  temperature,  as  does  a  mol  of  any 
other  substance  in  the  same  volume. 

The  value  of  the  above  will  be  appreciated  by  the 
following  adaptation  of  the  law  for  gases.  One  mol 
of  oxygen  (32  grams)  occupies  at  standard  pressure 
and  temperature  22.4  liters,  f  as  does,  by  Avogadro's 
law,  the  mol  of  any  other  gas.  If  now,  instead  of 
allowing  the  mol  to  occupy  22.4  liters,  we  compress 
it  into  one  liter,  the  pressure,  by  Mariotte's  law, 
becomes  22.4  atmospheres,  instead  of  i,  and  the 
volume  I,  instead  of  22.4  liters.  From  this,  since 
the  gas  laws  hold  for  solutions,  one  mol  of  any  sub- 
stance dissolved  in  one  liter  of  water  must  exert  an 
osmotic  pressure  of  22.4  atmospheres.  Accordingly 
then,  we  can  determine  molecular  weights  of  substances 

*Zeit.  f.  phys.  Chem.  I.  p.  481  (1887). 
f  i  gr.  O  —699.25  cc. 

32  gr.  O  =  (i  mol)  =  32  X  699.25  =  22.376  liters, 
or  in  round  numbers  22.4  liters. 


14  THE    THEORY   OF  SOLUTION. 

in  solution.  Thus  a  2%  solution  of  sugar  gives  an 
osmotic  pressure  of  IOI.6  cm.;  then  (2%  per  liter  = 
20  grms.) 

20  :  M  ::  IOI.6  :  (22.4  X  76). 
20 

M= 


while  theoretically  we  have  342  ;  a  very  good  agree- 
ment, considering  the  difficulties  with  the  semi-per- 
meable film. 

In  the  case  of  saltpeter,  and  all  other  inorganic  salts 
of  the  type,  these  laws  do  not  hold;  and  the  pressure 
is  always  greater  than  it  should  be.  Thus  de  Vries,* 
by  a  method  based  upon  the  behavior  of  plant-cells, 
found  that  solutions  of  sugar  and  saltpeter,  containing 
the  same  number  of  mols  in  equal  volumes,  gave 
osmotic  pressures  related  as  I  ;  1.6  (instead  of  as  I  :  i); 
and  the  more  dilute  the  solutions  were,  the  greater 
was  the  difference, 

Granting  now  that  sugar  and  other  organic  sub- 
stances act  normally  (which  has  since  been  proven), 
then  there  must  be  more  molecules  of  saltpeter  present 
than  there  should  be;  i.e.,  each  molecule  must  split  up 
into  two  or  more.  This  is  the  same  assumption  that 
we  had  to  make  for  gases.  In  that  case  the  number  of 
molecules  increased  and  so,  under  the  same  pressure, 
enlarged  the  volume.  In  the  case  of  solution,  how- 
ever, the  volume  (of  liquid)  remains  the  same,  and 
consequently  the  pressure  must  increase  in  the  same 
proportion,  as  the  volume  did  before. 

*  Pringsheims  Jahrbiich,  14.  427. 


THE    THEORY  0^  1 5 

Results,  by  the  method  of  osmotic  pressure,  are 
so  difficult  to  obtain  that  other  methods  have  been 
devised  which  depend,  in  principle,  upon  the  same 
factor  (concentration)  as  does  the  osmotic  pressure. 
These  are  used  now  in  its  place,  for  from  the  con- 
centration and  absolute  temperature  we  can  calcu- 
late, for  all  normal  substances,  the  osmotic  pressure. 

Further  work  upon  the  inorganic  salts,  by  all 
methods,  showed  conclusively  that  these  gave  pres- 
sures greater  than  they  should  give  by  the  law. 

Here,  however,  a  fact  was  discovered  by  Arrhenius 
that  led  to  the  theory  of  electrolytic  dissociation  in 
solution,  which  was  the  second  step  towards  our 
theory  of  solution,  osmotic  pressure  being  the  first. 
Arrhenius  found  that  those  substances,  and  only  those, 
which  give  abnormal  osmotic  pressures  are  capable  of 
conducting  the  electric  current;  and  if  these  substances 
are  dissolved  in  any  other  solvent,  in  'which  they  act 
normally,  they  lose  that  power. 

Before  going  farther,  we  will  consider  for  a  moment 
how  electricity  is  conducted  in  a  liquid,  in  order  to  see 
just  what  this  strange  action  means.  Grotthus  was 
the  first  to  discover  that  solutions  conduct  electricity 
in  a  manner  different  from  metals,  and  he  showed  that 
the  electricity  was  carried  bodily,  by  particles  of  the 
dissolved  substance,  from  one  pole  to  the  other. 
When  these  arrived  at  either  pole  they  dischaiged 
their  electricity;  when  the  current  was  broken  they 
disappeared  again  from  the  solution.  The  assumption 
was  then  that  the  current  first  decomposed  the  sub- 
stance into  smaller  particles,  and  that  these  then,  by 
electrostatic  attraction  and  repulsion,  moved  through 


l6  THE    THEORY  OF  SOLUTION. 

the  liquid,  carrying  their  charges  with  them.  Fara- 
day also  did  a  great  deal  of  work  upon  this  subject, 
and  gave  the  name  ions  to  the  particles,  and  gave  out 
and  proved  the  following  law,  which  is  the  basis  of 
all  electrochemical  work: 

.  All  movement  of  electricity  in  electrolytes  occurs 
only  by  the  concurrent  movement  of  the  ions;  and  in  the 
following  manner,  equal  amounts  of  electricity  move 
chemically  equivalent  amounts  of  the  different  ions. 

We  can  now  understand  what  Arrhenius'  discovery 
means.  He  found  that  all  substances  which  conduct 
electricity  (and  only  such)  give  abnormal  osmotic  pres- 
sures, i.e.,  have  too  great  a  number  of  molecules 
present.  We  know  that  all  substances  in  solution 
which  conduct  electricity  do  so  by  virtue  of  particles, 
which  are  formed  from  the  molecules  of  the  substance. 
Hence,  since  all  electrolytes  give  pressures  which  are 
too  high,  they  must  have  these  particles  (ions)  present 
in  them,  under  all  circumstances,  which  act  as  mole- 
cules, and  so  increase  the  osmotic  pressure.  This  is 
the  assumption  made  by  Arrhenius*  in  1887,  the 
process  which  produced  them  was  called  by  him 
electrolytic  dissociation.  In  the  next  section  we  will 
study  it  more  in  detail,  and  find  the  laws  which 
govern  it. 

ELECTROLYTIC  DISSOCIATION. 

Arrhenius  found  that  the  electrical  conductivity  of 
all  substances  increased  with  increasing  dilution  (i.e., 
decreasing  concentration).  That  is,  the  more  dilute 

*  Zeit.  f.  phys.  Chem.,  I.  631. 


..-    -• 

THE    THEORY   OF  SOLUTION.  IJ 

the  solution  is,  the  greater  the  proportion  of  ions 
present.  He  then  divided  the  molecules  in  solution 
into  two  groups,  the  inactive  ones,  or  molecules  which 
can  split  into  ions,  and  the  active  ones,  which  are  the 
ions.  The  first  do  not  take  any  part  in  conducting 
the  current,  that  being  done  by  the  ions  (active).  In 
the  case  of  osmotic  pressure,  however,  the  inactive 
as  well  as  the  active  ones  have  their  influence,  and  so 
dilute  solutions  should  give  results  more  abnormal  than 
others,  which  is  a  fact.  In  contrast  to  this,  all  sub- 
stances which  do  not  conduct  electricity  (sugar)  give 
normal  pressures,  for  there  is  no  dissociation  and  conse- 
quently no  ions,  and  the  pressure  is  caused  by  the  in- 
active molecules  alone.  The  osmotic  pressure,  then,  in 
a  solution  is,  as  it  is  for  a  gas  by  Dalton's  law,  the  sum 
of  the  individual  osmotic  pressures.  Unlike  ions,  then, 
added  to  a  solution  only  increase  the  total  pressure, 
while  like  ions  have  an  influence  upon  the  equilibrium, 
just  as  with  gases  (NH4C1),  as  will  be  explained  later. 
Arrhenius  called  the  ratio  of  the  ions  present  in  a 
certain  volume  to  those  at  infinite  volume  the  degree 
of  dissociation  (a)\  i.e., 


a  = 


where  JJV  and  nj*  are  the  so-called  molecular  conduc- 
tivities at  the  two  volumes  v  and  v^.  The  molecular 
conductivity  is  found  by  multiplying  the  specific  con- 
ductivity. expressed  in  terms  of  the  conductivity  of  a 
column  of  mercury,  by  the  molecular  weight.  The 

*To  find  ^  see  Chap.  II. 


1 8  THE    THEORY  OF  SOLUTION. 

value  of  a  is  found  to  increase  with  the  dilution. 
This  does  not  mean  that  there  are  more  ions  present  in 
a  dilute  than  in  a  strong  solution,  but  that  the  propor- 
tion is  greater.  In  a  dilute  solution  we  would  thus 
have  a  larger  proportion  of  a  smaller  total  number, 
and  vice  versa  for  a  strong  one;  the  latter,  in  each 
case,  would  thus  have  the  greater  absolute  number 
of  ions,  but  would  have,  in  proportion,  a  larger  num- 
ber of  inactive  molecules. 

At  this  time  it  was  found  that  these  ions  were  also 
the  active  members  in  chemical  reactions,  and  that,  in 
a  solution  of  a  substance,  only  those  elements  present 
as  ions  gave  their  characteristic  reactions.  Thus  in 
the  case  of  CH8C1,  which  dissociates  into  CH2C1  and 
H,  no  reaction  for  chlorine  with  AgNO,  can  be 
obtained  until  the  complex  ion  CH,C1  is  decomposed, 
Cl  ions  set  free.  The  power  to  conduct  electricity 
and  chemical  affinity  are  thus  closely  related,  and 
the  value  of  the  one  gives  that  of  the  other;  for 
both  depend  upon  the  same  condition,  i.e.,  the  pres- 
ence of  ions. 

We  have  thus  far  followed  logically  and  historically 
the  development  of  the  theory  of  solution,  as  based 
upon  the  electrolytic  dissociation,  from  the  laws 
governing  the  behavior  of  gases,  and  have  seen  how 
each  fact  has  led  to  a  new  assumption,  and  this  by 
being  proven  has  in  turn  led  to  another.  We  will  now 
drop  this  method  of  treatment,  and  give  simply  the 
results  of  the  modern  investigations,  and  thus  gain  a 
view  of  the  perfected  theory  as  it  exists  to-day. 

In  the  first  place  we  will  state  that  important  law, 
as  discovered  by  Kohlrausch,  which  he  calls  the  Law 


THE    THEORY   OF  SOLUTION-.  19 

of  the  Independent  Wandering  of  tJie  Ions.  According 
to  it  the  movements  of  an  ion  are  independent  of  those 
with  which  it  is  in  equilibrium.  That  is,  a  chlorine 
ion  moves  with  the  same  velocity  (and  each  ion  has  a 
certain  velocity  in  water,  which  has  been  determined) 
when  in  combination  with  hydrogen  ions  as  it  does 
when  with  ions  of  sodium  or  any  other  substance. 

By  Faraday's  law  each  ion  can  carry  with  it  a  cer- 
tain amount  of  electricity;  so  that  this,  in  combination 
with  the  above,  shows  that  each  ion  always  carries  the 
same  amount  of  electricity  no  matter  in  what  com- 
bination it  exists.  It  has  been  found  necessary  to 
assume  that  as  soon  as  a  substance  dissolves  and  dis- 
sociates the  ions  receive  enormous  charges  of  elec- 
tricity* (calculated  below  by  Faraday's  law),  and  that 
one  is  negatively  and  the  other  positively  charged, 
in  a  binary  electrolyte,  and  with  equal  amounts  of 
electricity  (-)-  and  — ). 

With  one  gram  of  hydrogen  ions  (Faraday's  law) 
there  are  96537  coulombs  of  electricity  carried;  conse- 
quently one  coulomb  causes  o.ooooi  gram  of  hydro- 
gen ions  to  move.  Thus  to  prove  that  the  ions  are 
charged  with  electricity  is  an  extremely  difficult  thing, 
for  the  charges  are  so  large  for  infinitely  small  amounts 
of  substance;  but  Ostwald  and  Nernst  f  have  proved 


*  This  is  not  so  hard  to  believe  as  many  have  tried  10  make  it 
for  we  know  that  dissociation  can  only  take  place  when  equal 
amounts  of  positive  and  negative  electricity  are  given  to  the  ions. 
As  to  the  enormous  charges,  they  can  be  explained  in  the  same 
manner  as  is  the  fact  that  from  a  piece  of  amber,  by  rubbing  we 
can  obtain  an  almost  infinite  amount  of  static  electricity.  The 
actions  are  probably  somewhat  similar. 

fZeit.  f    phvs.  Chen,,  III. 


UNIVERSITY 

X.  /SAI   .•L.KIlk.       ^S 


20  THE    THEORY  OF  SOLUTION. 

it  notwithstanding  by  very  delicate  apparatus.  Later 
we  will  see  how  the  considerations  of  a  voltaic  cell  also 
go  to  prove  it. 

The  simplest  way  of  grasping  the  theory  will  be  to 
study  the  state  of  a  dilute  solution,  and  see  how  it 
acts  chemically  and  electrically.  We  will  consider  a 
dilute  solution  of  sodium  chloride  (i  mol  to  10,000 
liters);  here,  practically,  we  have  complete  dissocia- 
tion, according  to  the  scheme 

«/•  ;  /DO  oo  *OQ  , 

NaCl  =  Na  +  Cl. 


The  signs  *  and  '  stand  respectively  for  the  number 
of  equivalents  of  positive  and  negative  electricity. 
Thus  for  Ca  we  have  two  positive  ones,  Ca;  and  for 
SO4  two  negative  ones,  SO4. 

It  is  hard  to  imagine  free  sodium  and  free  chlorine 

j      to  exist  in  water;  but  we  must  remember  that  these 

are    ions,    and    charged    with    enormous    amounts    of 

electricity,   and  consequently  different  from  the  ele- 

-v,?  ments  as  we  know  them.     This  will  remove  the  diffi- 

culty, particularly  when  we  find  that,  on  losing  their 

K*  charges  (by  electrolysis),  they  again  assume  their  well- 

1)  ^     known  properties,  and  the  Na  decomposes  the  water 

^o    and  gives  off  H  gas  at  one  pole,  while  Cl  gas  is  given 

?  V    off  at  the  other. 

If  now  we  place  two  platinum  plates,  connected  with 
a  source  of  electricity,  in  this  solution,  and  pass  the 
current  through  it,  the  following  action  takes  place. 
First  the  plates  become  charged,  and  these  charges 

rwork  electrostatically  upon  the  charged  ions  of  the 
solution.  The  positive  ions  (Na)  will  be  attracted  by 


THE    THEORY  OF  SOLUTION.  21 

the  negatively  charged  plate  and  repelled  by  the 
other;  the  negative  ions  (Cl)  on  the  other  hand  will 
be  attracted  by  the  positive  plate  and  repelled  by  the 
negative.  In  this  way  the  positive  and  negative  ions 
will  be  separated  (to  an  amount  equal  to  the  difference 
between  the  electrostatic  power  of  the  plates  and  that 
of  the  unlike  ions,  for  these  attract  one  another),  and 
a  storing  up  of  ions  will  take  place  on  either  plate. 
When  the  potential  becomes  high  enough,  the  attrac- 
tion of  the  plates  will  become  so  great  as  to  rob  the 
ions  (in  equivalent  amounts)  of  their  electricity  (-f-  and 
— )  and  the  current  flows  and  the  elements  (Na  (or  H) 
and  Cl)  appear. 

Before  a  current  passes  through,  the  charged  (-(- 
and  — )  ions  will  have  been  arranged  in  a  state  of  equi- 
librium. Afterwards,  however,  if  the  current  is  broken, 
like  ions  will  be  together,  and,  as  they  repel  one 
another,  a  new  equilibrium  will  be  established.  As 
no  one  ion  has  ever  been  found  to  act  as  both  positive 
and  negative,  elements  in  solution  are  never  dis- 
sociated. A  solvent  always  seems  to  be  necessary,  for 
molten  salts  do  not  conduct  electricity  to  a  very  great 
extent. 

When  water  is  placed  on  sodium  chloride,  the  action 
which  takes  place  is  exactly  analogous  to  that  of  the 
dissociation  of  solid  NH4C1.  The  volume  of  the  sol- 
vent here  being  the  volume,  in  which  the  substance  is 
confined.  Molecules  of  sodium  chloride  go  into  solu- 
tion, and  there  dissociate  into  Na  and  Cl  ions.  This 
process  continues  until  a  certain  osmotic  pressure  (for 
that  temperature)  is  reached  for  each  of  the  three 
members,  NaCl,  Na,  and  Cl,  when  it  ceases.  If  we 


22  THE    THEORY  OF  SOLUTION. 

enlarge  the  volume  (i.e.,  add  water),  more  salt  dis- 
solves and  more  NaCl  molecules  dissociate,  until  the 
osmotic  pressures  are  the  same  as  before  (at  that  tem- 
perature). Ostwald  proved,  by  means  of  the  electrical 
conductivity,  that  the  relation  between  the  dissociated 
portions  arid  the  undissociated  one  is  expressed,  for 
binary  electrolytes,  by  the  equation 

•  I 

KC  =  c,ca,   ct-  no      cv- 

where  C  is  the  concentration  of  the  undissociated  part, 
expressed  by  the  number  of  mols  per  liter;  C,  and  C, 
those  of  the  two  ions(+  and  —  );  and  K  is  a  constant, 
called  the  dissociation  constant,  which  depends  in 
value  upon  the  temperature. 

If  we  add  now  to  our  solution  of  sodium  chloride, 
another  chloride,  as  that  of  potassium,  what  will  be 
the  action  ?  The  ions  of  potassium  will  exert  no  in-. 
fluence  upon  the  reaction  (as  has  been  proven  by 
experiment),  but  the  Cl  ions^will  be  increased  in  con- 
centration, and  the  equilibrium  disturbed.  Before 
adding  KC1,  our  equilibrium  is%  expressed  by  the 
formula 

KC  =  QC,. 

C,  —  Cl  ions.  If  now  we  add  Cl  ions  in  a'  concen- 
tration C0,  our  formula  will  be  transformed  into 


In  the  first  equation  C  +  C,  =  A,  the  total  concen- 
tration of  the   NaCl;  .in   the   second   C'  +  C'a   must 


THE    THEORY  OF  SOLUTION.        .  23 

c>c_ 

again  =  A,  consequently  C'  must  be  larger  than  C 
(and  C,  >  C',),  for  K  is  a  constant.  That  means  that 
the  dissociation  goes  back  and  the  undissociated  por- 
tion increases,  just  as  it  did  with  gaseous  dissociation. 
(NH4C1).  This  was  proven  experimentally  by  Ar- 
rhenius*  for  acetic  acid  and  sodium  acetate,  and  a 
number  of  other  salts.  By  aid  of  this  formula  it  is 
possible  to  find  C0,  i.e.,  the  concentration  of  added 
Cl  ions,  by  solving  the  equation  for  C0.  In  general, 
then,  tJie  addition  of  an  indifferent  ion  has  no  effect  upon 
the  equilibrium;  while  that  of  a  like  ion  drives  back  the 
dissociation  to  the  amount  expressed  in  our  formula. 
We  must  keep  in  mind  here  that  when  an  ion  is 
driven  back  into  the  undissociated  portion,  it  takes 
with  it  the  other  ion,  with  which  it  was  in  equilibrium. 
Thus  in  our  formulae  C'2  is  smaller  than  Ca ,  and  in 
the  same  degree  is  C',  smaller  than  Q. 

We  will  now  consider  the  case  of  water  and  what 
effect  its  slight  dissociation  has  upon  chemical  reac- 
tions. At  first  water  was  thought  to  be  undissociated, 
but  Kohlrausch  found  it  to  be  dissociated  to  a  very 
small  extent.  This  fact"  makes  clear  one  chemical 
phenomenon  that  could  never  be  explained  before. 
When  strong  acids  neutralize  bases,  it  was  observed 
that  the  same  amount  of  heat  was  developed.  This 
is  now  quite  easy  to  understand;  the  reaction,  for 
example, 

HC1  +  KOH  =  HaO  +  KC1, 
*Zeit.  f.  phys.  Chem.,  V.  i  (1890). 


24  THE    THEORY  OF  SOLUTION. 

written  with  respect  to  the  ions,  becomes: 

•  H  +  C'l  +  K  +  OH  =  HaO  +  K  +  Cl. 

That  is,  H  and  OH  ions  cannot  exist  beside  one 
another  (except  to  a  very  slight  extent)  and  thus  unite 
and  form  undissociated  water;  the  K  and  Cl  re- 
maining in  the  ionic  state.  Most  of  the  strong  acids 
contain  the  same  number  of  H  ions  in  equal  volumes, 
and  so,  with  equivalent  amounts  of  each,  the  same 
amount  of  water  is  formed,  and  hence  the  heat  is  the 
same.  This  is  found  to  be  true  for  all  acids  and 
bases  when  their  degrees  of  dissociation  are  taken 
into  consideration.  Thus  if  an  acid  is  dissociated  in 
such  a  way  as  to  have  present,  for  equal  volumes,  but 
one  half  the  number  of  H  ions  that  HC1  has,  then  the 
heat  is  but  one  half  as  great,  for  but  one  half  the 

amount  of  water  is  formed.     Just  so  with  the  bases. 

i  •  H 

The  ions  of  water  are  H  and  OH,  and  not  HH  and  O 
as  one  might  suppose.  The  effect  produced  by  the 
fact  that  water  is  but  slightly  dissociated  can  be  more 
clearly  understood  from  the  following  example.  Since 
the  dissociation  constant,  for  water,  is  very  small, 
only  a  very  small  number  of  ions  of  OH  and  H  can 
exist  together;  in  other  words,  if  they  are  placed 
together  they  unite  and  form,  as  above,  undissociated 
water.  Thus  if  we  have  a  hydroxide  of  an  element  in 
solid  form,  in  water,  ions  of  the  element  and  of  OH  are 
present,  to  a  certain  degree  (even  though  it  be  small), 
and  the  addition  of  an  acid,  i.e.,  free  hydrogen  ions, 
must  form  undissociated  water,  and  a  dissociated  salt 
of  the  element  with  the  negative  element  of  the  acid. 


UJNIVERSITT) 

^^SAJJORNJ^^ 

THE  THEORY  OF  SOLUTJUTTT  2$ 

By  this,  however,  OH  ions  disappear  and  more  are 
formed  and  used,  and  again  more  are  formed,  etc.  In 
this  way  each  new  dissociation  gives  off  ions  of  the 
metal,  these  form  an  equilibrium  with  the  negative 
ion  of  the  acid,  and  finally,  if  enough  acid  is  added, 
the  hydroxide  goes  into  solution,  forming  a  salt  (dis- 
sociated) and  water.  ,» 

When  a  substance  dissociates  into  *a  simple  and  a 
complex  ion,  the  general  rule  is  that  by  increasing  the 
dilution  (decreasing  the  concentration)  some  of  the 
substance  dissociates  further,  to  a  very  small  extent, 
into  its  ultimate  ions.  Thus 

H2SO4  =  H  +  HSO4  , 
and,  to  a  very  small  extent, 

H2SO4  =  HH  +  SO, 

which  amount  increases  with  decreasing  concentration. 
Also 

H3P04  =  H  +  H2P04 
and 

H3PO4  =  H  +  H  +  HPO4 

to  a  small  extent. 

This  is  also  true  with  regard  to  KAgCN3  and  salts 
of  that  description.  Thus 


then  to  a  lesser  degree, 

Rotassium  -f-  AgCN2  =  Potassium  +  AgCN  +  CN, 


26  THE    THEORY  OF  SOLUTION. 

where  AgCN  is  neutral,  and  this  then  dissociates,  to  a 
very  slight  extent  indeed,  into 

AgCN  =  Ag+CN. 

In  a  i/io  normal  solution,  the  first  step  is  nearly 
complete;  the  second  to  a  degree  that  the  CN  ions 
have  a  concentration  of  2.76  X  io~3  normal,  i.e., 
about  5$  dissociated;  and  the  third  to  a  concentration 
of  Ag  ions  of  3.65  X  io~"  normal.* 

So  much  for  the  present  for  electrolytic  dissociation 
itself,  but,  as  later  in  each  of  the  other  chapters  it  is 
the  basis  of  our  work,  a  number  of  new  aspects  of  it 
will  be  developed  which  can  find  no  place  here. 

*  The  author.     Zeit.  f.  Phys.  Chem.,  XVII.  513-535(1895). 


CHAPTER   II. 

METHODS     FOR    THE    DETERMINATION   OF   ELEC- 
TROLYTIC  DISSOCIATION.* 

THESE  methods  can  be  divided  into  three  groups. 
I  will  describe  those  in  each  group,  as  far  as  concerns 
the  principles  upon  which  they  are  based,  and  will 
refer  the  reader  elsewhere  for  details. 

FIRST  'GROUP. — Osmotic  Pressure,  Lowering  of  the 
Freezing-point,  Increase  of  the  Boiling-point,  etc. 
These  methods  are  not  as  valuable  as  those  of  the 
other  two  gr-oups;  as  not  only  the  number  of  ions, 
but  also  the  number  of  inactive  molecules,  are  found 
by  them.  We  have  considered  osmotic  pressure 
already,  so  we  will  first  turn  to  the  freezing-point 
method.  In  the  last  century  it  was  found  that  the 
addition  of  a  soluble  substance  to  a  liquid  lowered 
the  freezing-point  of  the  same,  and  this  lowering 
was  proportional  to  the  amount  of  substance  added. 
In  1884  Raoult  improved  the  method,  and  found 
that  one  mol  of  any  substance  like  sugar  (undis- 
sociated  as  we  now  know  them  to  be)  in  one  hun- 
dred mols  of  solvent  lowered  the  freezing-point  of 
the  same  0.63°  C.  For  an  electrolyte  (dissociated 

*  For  details  see  Ostwald,   Hand-  und    Hilfsbuch  zur  ausfiih- 
rung  Physiko-chemischer  Messungen  (Leipzig,  1893). 

27 


28  THE   THEORY  OF  SOLUTION. 

substance),  if  the  molecular  weight  is  known,  this 
method  can  be  used  to  determine  the  degree  of  dis- 
sociation; while  for  a  non-electrolyte  whose  molecular 
weight  is  unknown,  the  method  can  be  used  to  find  it. 

Thus  if  an  electrolyte  in  solution,  I  mol  to  100  mols 
of  water  =  iSoogrms.,  gives  a  lowering  of  1.2°  C.,  then 
there  must  be  nearly  two  mols  present  and  hence  the 
substance  is  nearly  completely  dissociated.  The  re- 
sults, for  small  degrees  of  dissociation,  are  complicated 
by  the  action  of  the  inactive  molecules,  and  the  latter 
in  strong  solutions  may  form  more  complex  molecules, 
which  would  further  affect  the  results.  The  apparatus 
of  Beckmann  consists,  in  principle,  of  a  tube,  a  deli- 
cate thermometer,  and  a  freezing  bath.  The  freezing- 
point  of  the  pure  solvent  is  first  determined,  and  then 
a  weighed  amount  of  the  substance  added  and  the 
freezing-point  of  the  solution  found.  The  difference 
in  the  two  is  proportional  of  course  to  the  amount  of 
substance  added;  and  from  it,  the  weight  of  substance 
added,  and  the  molecular  weight,  we  can  find  the  de- 
gree of  dissociation. 

The  boiling-point  method  is  based  upon  the  same 
principle  as  that  of  the  freezing-point.  When  we  add 
substance  to  a  solvent,  the  boiling-point  of  the  same 
is  increased  by  an  amount  proportional  to  the  amount 
of  substance  added.  Beckmann  has  also  devised  an 
apparatus  for  this  purpose.  A  solvent  which  has  a 
low  boiling-point,  as  ether,  is  usually  used,  and  as 
almost  no  dissociation  takes  place  in  it,  the  method 
gives  normal  results  and  so  is  employed  principally  for 
determining  molecular  weights  and  not  dissociation. 

SECOND  GROUP. — The  method  of  this  group  is  that 


ELECTROL  YT1C  D  IS  SO  CIA  TION.  2g 

of  electrical  conductivity,  as  originated  by  Kohlrausch 
and  Ostwald.  We  know  that  only  the  ions  conduct 
electricity,  and  that  at  infinite  dilution  only  ions  are 
present,  and  consequently  the  ratio  of  conductivity  at 
a  certain  volume,  to  that  at  infinite  volume  gives  the 
ratio  of  free  ions  present  to  those  that  could  be 
present,  i.e.  the  degree  of  dissociation  (#).  We  have 
then 


ft* 

Of  course,  as  it  is  a  ratio,  the  specific  conductivity 
might  be  used,  but  it  is  always  well  to  use,  as  above, 
the  molecular  conductivity,  for  salts  of  the  same  series 
(and  acids  also)  have  almost  the  same  molecular 
conductivity;  and  in  addition  we  usually  find  the  term 
/^  in  those  units. 

The  apparatus  consists  of  a  glass  vessel,  in  which  the 
solution  is  placed,  which  is  provided  with  platinum 
electrodes.  The  arrangement  is  the  ordinary  one  for 
determining  the  electrical  resistance  (reciprocal  of 
conductivity),  except  that  an  induction-coil  and  tele- 
phone receiver  are  used  to  find  the  neutral  point  in 
place  of  the  flowing  current  and  galvanometer.  If  a 
flowing  current  were  used,  electrolysis  would  take 
place  and  the  elements  would  appear  at  the  electrodes, 
thus  decreasing  the  concentration  and  causing  the 
conductivit}7  to  vary.  With  the  alternating  current, 
however,  all  the  substance  separated  out  by  the  stream 
in  one  direction  will  redissolve  when  the  direction 
of  the  current  is  reversed,  and  consequently  the  poles 
are  changed,  and  the  conductivity  is  constant, 


30  THE    THEORY  OF  SOLUTION. 

For  this  purpose,  then,  the  current  from  a  battery  is 
passed  through  the  current-breaker,  and  then  sent 
through  the  cell,  which  is  connected  to  a  rheostat  and 
regular  Wheatstone  bridge  arrangement.  When  the 
buzzing  in  the  telephone  is  at  a  minimum,  then  the 
resistance  of  the  cell  is  equal  to  a  certain  part,  as 
shown  on  the  bridge,  of  the  rheostat  resistance,  and 
so  we  can  easily  calculate  the  resistances  of  the  cell. 
The  conductivity  is  the  reciprocal  of  the  resistance; 
the  specific  conductivity  multiplied  by  the  molecular 
weight  is  the  molecular  conductivity,  and  is  the  sum  of 
the  molecular  conductivities  of  the  ions  (present  in 
that  volume)  of  which  it  is  composed.  The  conduc- 
tivity varies  greatly  with  the  temperature,  and  so  this 
must  be  kept  constant  to  i/io  of  i°  C.  during  the 
measurement.  The  value  /^  can  be  found  by  adding 
together  the  molecular  conductivities  (for  infinite  dilu- 
tion) of  the  ions  of  which  the  substance  is  composed.* 
Kohlrausch,  by  aid  of  his  law  of  independent  wander- 
ing of  the  ions,  has  determined  this  value  for  all 
ions,  and  so  we  can  take  the  necessary  values  from 
the  table  and  add  them  together,  and  we  have  the 
desired  value.  In  many  cases  it  is  possible  to  attain 
this  state  practically,  and  the  results  so  obtained  agree 
very  well  with  those  calculated. 
According  to  Kohlrausch's  law, 

ux=  u-\-  v, 


*  In  calculating  theoretically  the  ^values  juv  and  //„,  we  take 
for  //j,  the  sum  of  the  molecular  conductivities  of  the  ions  and 
multiply  it  by  a.  n^  is  where  a  =  i. 

Py  =  (mol.  cond.  of  -f-  ion  +  mol.  cond.  of  —  ion)cr, 


ELECTROLYTIC  DISSOCIATION.  31 

where  u  and  v  are  the  molecular  conductivities  of  the 
two  ions,  and  JJL  is  the  molecular  conductivity,  at 
infinite  volume,  of  the  substance.  We  can  find,  by 
altering  this  equation  slightly,  the  value  for  /*  at  any 
dilution  (see  page  30,  note)  if  we  know  v/hat  value  a 
has  for  it.  Thus 


In   the   first  case   a  =  i,    and   we  have  JHM  =  u  -\-  v, 
as  above. 

In  the  last  chapter  it  was  said  that  Ostwald  proved 
the  equation 


where  C  =  mols  (or  fraction  of  a  mol)  of  undissociated 
substance  per  liter;  C,  and  C2  being  those  of  the  two 
ions,  and  K  is  the  dissociation  constant.  He  did  this 
by  aid  of  the  conductivity,  but  with  the  equation  in  a 
different  form  than  the  above.  It  is  more  convenient  to 
use  dilution,  instead  of  concentration,  particularly  for 
dilute  solutions.  Thus  instead  of  speaking  of  a  sub- 
stance as  i/io  normal,  it  is  simpler  to  say  a  dilution 
of  10  liters  (i.e.,  the  number  of  liters  in  which  one 
mol  is  dissolved).  Then,  again,  since  molecular  con- 
ductivity varies  directly  with  dilution  (inversely  with 
concentration),  it  is  clearer  to  have  it  as  a  term  in  our 
equation.  We  will  now  transform  this  equation  and 
get  it  in  the  form  that  Ostwald  did,  and  show  how  he 
proved  K  to  be  a  constant.  Our  formula  to  start 
with  is 

KC  =  C.C,. 


32  THE    THEORY  OF  SOLUTION. 

Let  us  suppose  the  total  amount  of  substance  dissolved 
is  equal  to  I  ;   then,  a  =  degree  of  dissociation, 


a  -c 

v         " 


or 


v(i  -  or)' 


K  = 


But     a=  —  ;      .-.  K  = 


This  is  the  formula  used  by  Ostwald,  and  by  it  he 
tound  K  to  be  constant  for  all  the  weaker  acids,  but 
not  so  for  the  stronger  ones,  as  HC1.  The  reason  for 
this  is  still  unexplained.  The  value  of  K  for  the 
organic  acids  is  larger  or  smaller  as  the  acids  are 
stronger  or  weaker.  It  is  thus  a  measure  of  the 
chemical  affinity  of  substances.  To  give  some  idea 
of  the  size  of  this  constant,  a  few  examples  are  given. 

Formic  Acid. 
ju«  =  376;    IOOK  =  k  —  0.0214. 

Acetic  Acid 
//<*  —  364;    IOOK  =  k  =  0.00180. 

Butyric  Acid. 
yuoo  =  359;    IOOK  =  k  =  0.00134. 


ELECTRQL  YTIC  DISSOCIA  TION.  33 

These  values  are  the  means  of  a  long  series  of 
determinations.  As  will  be  seen,  the  three  examples 
given  above  are  placed  in  order  of  their  activity, 
formic  acid  being  the  most  active,  and  so  its  constant 
is  the  largest;  but  this  is  merely  another  way  of  say- 
ing that  it  has  more  H  ions  present  in  it  than  the 
others. 

THIRD  GROUP.  —  To  this  group  belong  all  methods 
which  allow  us  to  determine  the  presence  of  one  ion, 
and  its  amount.  If  there  is  but  one  other  ion,  in 
equilibrium  with  it,  to  form  the  undissociated  portion, 
then  ions  of  other  kinds  added  to  the  solution  will 
have  no  effect  upon  the  equilibrium.  The  effect  of 
adding  an  amount  of  the  ion,  with  which  it  is  in  equi- 
librium, has  already  been  pointed  out.  This  princi- 
ple we  will  use  later.  These  methods  are  of  great 
value  to  us,  for  they  allow  us  to  follow  the  course  of 
the  dissociation,  and  to  ascertain  just  what  ions  are 
present  and  to  what  concentration.  The  methods 
are  restricted,  however,  at  present  to  the  determina- 
tion of  but  a  few  ions;  but  soon  we  may  hope  to  have 
all  those  necessary  to  follow  any  reaction. 

For  a  long  time  it  has  been  known  that  addition  of 
acid  to  a  sugar  solution  accelerates  the  rapidity  of 
its  inversion,  as  the  breaking  down  into  dextrose  and 
laevulose  is  called.  The  rapidity  depends  upon  the 
strength  of  the  acid  used;  and  as  this  depends  upon 
the  number  of  hydrogen  ions  present,  the  rapidity 
must  also.  The  reaction  is  a  strange  one,  for  the  acid 
does  not  change  its  composition,  and  the  same  amount 
is  present  after  the  action  has  ceased,  as  before.  Such 
an  action  is  called  a  catalytic  one.  Trevor  made 


OF  THE 

UNIVERSITY1 


34  THE    THEORY  OF  SOLUTION. 

of  this  catalytic  action  of  hydrogen  ions  upon  the 
inversion  of  cane-sugar  to  determine  the  concentra- 
tion of  the  H  ions,  and  with  very  good  success.  He 
worked  at  100°  C.,  starting  with  a  solution  of  sugar 
whose  strength  he  determined  by  aid  of  a  polariscope; 
he  then  determined  it  after  intervals  of  time,  and  thus 
found  the  velocity  of  change  without  acid.  Then  by 
adding  acid  solutions  containing  a  known  strength  of 
H  ions,  and  determining  again  the  amount  of  sugar 
present,  he  was  able  to  find  just  what  effect  a  certain 
amount  of  hydrogen  in  ionic  form  had,  and  to  form  an 
equation  expressing  it.  Of  course,  then,  it  was  possi- 
ble to  determine  unknown  amounts,  and  this  he  did 
in  a  large  number  of  cases.  Thus  we  have  one  good 
method  for  determining  H  ions;  and  there  is  another 
still,  devised  by  Ostwald,  which  depends  upon  the 
E.M.F.  of  a  Grove  gas-cell,  but  farther  into  that  we 
will  not  go. 

In  the  next  chapter  is  described  a  method,  by 
Ostwald,  for  determining  dissociation  by  aid  of  the 
electromotive  force  of  a  specially  prepared  cell.  This 
allows  us  to  determine  the  concentration  of  ions  of  all 
metals,  as  long  as  they  give  good  constant  electrodes, 
as,  for  example,  silver.  This  method  can  also  be  ex- 
panded for  negative  ions.  By  it  the  author*  was 
able  to  determine  Cu  ions  and  also  the  dissociation 
constant  of  hydrocyanic  acid,  a  number  too  small  to 
be  accurately  determined  by  any  other  method.  We 
will  take  it  for  granted,  then,  that  the  concentration  of 
Ag  ions  in  KAgCN,  can  be  determined  by  aid  of  the 

*  Zeit.  f.  Phys.  Chem.,  XVII.  513-535  (1895). 


ELECTROLYTIC  DISSOCIATION.  35 

E.M.F.,  and  explain  the  principle  of  the  method. 
Silver  ions  are  in  equilibrium  here  (Chap.  I)  with  CN 
ions.  If  we  add  to  the  solution  a  substance  contain- 
ing CN  ions,  those  of  Ag  will  be  driven  back  propor- 
tionally. By  determining  this  new  concentration  of 
Ag  ions,  that  of  the  CN  ions  added  can  be  found. 
A  formula,  however,  cannot  be  used  here,  on  account 
of  the  large  amount  of  CN  ions  which  are  present,  and 
yet  are  not  in  equilibrium  with  the  Ag,  to  form  un- 
dissociated  AgCN.  A  solution  of  sodium  cyanide  of 
known  dissociation  was  then  used,  and  its  effect  on 
the  Ag  ions  of  the  KAgCN2  noted,  and  the  relation 
expressed  by  means  of  a  curve,  of  which  E.M.F.  and 
concentration  of  CN  ions  were  the  coordinates.  In 
this  way,  after  adding  CN  ions,  the  E.M.F.  was  deter- 
mined and  the  amount  of  CN  ions  found  by  interpola- 
tion. Of  course  the  KAgCN2  solution  was  always  kept 
at  the  same  concentration.  By  aid  of  some  compound 
(of  the  nature  of  KAgCNJ  containing  Cl  or  other  ions, 
these  also  could  be  determined. 


CHAPTER    III. 
THE   THEORY   OF   THE   VOLTAIC   CELL. 

IN  our  first  chapter  an  outline  of  the  new  theory  of 
solution,  as  based  upon  electrolytic  dissociation,  was 
given  in  brief.  In  the  present  chapter  we  will  see 
what  a  great  influence  it  has  had  upon  the  theory  of 
electric  batteries,  and  what  new  insight  it  has  given 
us  concerning  the  ways  of  electrical  energy  and  its 
relations  to  chemical  energy. 

According  to  the  law  of  the  conservation  of  energy, 
the  electricity  generated  in  a  reversible  battery  is 
equal  to  the  energy  generated  by  the  chemical  reac- 
tion which  takes  place  in  it.  In  other  words,  the 
energy  of  the  chemical  reaction,  turned  into  electrical 
units,  is  the  energy  of  the  cell.  Thus,  for  example, 
in  the  Daniell  battery  of  zinc  in  zinc  sulphate,  and 
copper  in  copper  sulphate,  the  chemical  process  con- 
sists in  dissolving  the  Zn  and  separating  Cu.  The 
formula  is 

Zn  +  Cu  +  SO4  =  Zn  +  SO4  +  Cu. 

The  chemical  energy  (expressed  as  heat)  is  here   501 
calories  (K*),  while   the  electrical  energy,   volts  (ex- 

*  K  as  used  by  Ostwald  =  100  cals. 

36 


THE    THEORY  OF   THE    VOLTAIC  CELL.  37 

pressed  as  heat),  is  505  K.  This  shows  that  the 
theory  as  above  sketched  is  correct;  but  with  most 
other  combinations  widely  differing  results  are  ob- 
tained. But  this  has  been  shown  to  be  due  to  the 
temperature  coefficient  of  the  cell.  At  —  273°  C.  (ab- 
solute zero)  the  chemical  energy  is  always  equal  to  the 
electrical,  but  at  higher  temperatures  the  electrical  is 
usually  higher.  In  the  case  of  the  Daniell  cell  this 
coefficient  is  very  small,  and  so  makes  little  difference. 
The  relation  is 

Ee=  £c  +  e0 


where  Ee  =  electrical  energy  ; 
Ec  =  chemical        '  ' 
e0  =  amount  of  electricity; 

~TJ-'=-  rise  m  potential  n  for  i°  absolute  tem- 
perature. 

We  will  now  consider  what  takes  place  between  two 
solutions  of  the  same  substance  but  of  different 
strength. 

According  to  Faraday's  law,  differences  of  poten- 
tial in  electrolytes  are  only  possible  by  irregular 
arrangement  of  the  ions,  in  such  a  way  that  one  place 
has  an  excess  of  positive  ions,  and  another  an  excess  of 
negative  ones. 

Wherever  such  an  irregularity  is  found  we  must  find 
there  a  difference  of  electrical  potential,  i.e.,  an  electro- 
motive force.  Such  a  state  as  this  was  first  recognized 

*  Ostwald,  Lehrbuch  der  allg.  Chem.,  II.  819. 


38  THE    THEORY  OF  SOLUTION. 

by  Nernst*  as  due  to  the  unequal  velocity  of  the  ions 
in  a  solution  (Chap.  I).  If,  for  instance,  over  a  solu- 
tion of  hydrochloric  acid  we  have  a  very  dilute  solu- 
tion of  the  same,  then  in  the  strong  solution  both 
ions  H  and  Cl  will  be  present  in  the  same  number  and 
under  the  same  osmotic  pressure,  and  consequently 
driven  with  the  same  force  into  the  dilute  solution. 
Their  velocities  are,  however,  as  we  know,  different; 
and  so  this  produces  a  separation  of  the  ions  and  con- 
sequently a  difference  of  potential  between  the  solu- 
tions. In  this,  however,  electrostatic  attraction  and 
repulsion  enters  into  account  (for  like  ions  all  go  in  the 
same  direction),  which  retards  the  faster  ions  and  accel- 
erates the  slower  ones  until  the  velocities  have  been 
equalized,  when  it  ceases.  The  more  dilute  solution 
must  then  acquire  the  polarity  of  the  fastest  ion. 
Since  H  and  OH  are  the  fastest  ions,  every  acid  must 
be  negative  against  a  more  dilute  solution  of  the  same, 
and  every  base  positive. 

This  explains  those  momentary  differences  of  poten- 
tial which  are  so  often  observed,  and  which  then  sud- 
denly disappear.  This  E.M.F.  can  be  calculated  by 
means  of  a  formula,  and  Nernst  has  done  it  and  found 
the  explanation  to  be  the  correct  one. 

We  will  now  consider  a  constant  which  belongs  to 
each  metal,  and  which  will  help  us  to  understand  the 
process  which  takes  place  at  each  electrode.  Let  us 
imagine  a  metal  in  a  solution  of  one  of  its  salts;  it 
must  either  dissolve,  precipitate  the  ions  out  of  the 
solution  upon  itself,  or  remain  unaltered.  Therefore 

*Zeit.  f.  Phys.  Chem.,  II.  617  (1887). 


THE    THEORY  OF  THE    VOLTAIC  CELL.  39 

Nernst  ascribes  to  each  metal  a  certain  pressure,  P, 
with  which  it  strives  to  send  its  ions  into  the  solution. 
If/,  the  osmotic  pressure  of  the  metal  ions  in  the  solu- 
tion, is  less  than  this,  the  metal  dissolves  to  a  certain 
extent;  if  equal,  nothing  happens;  and  if  greater, 
metal  ions  go  from  the  solution  and  give  up  their  elec- 
tricity to  the  electrode  and  become  metallic.  This 
pressure,  P,  is  called  by  Nernst  the  electrolytic  tension 
of  solution.  It  is  a  constant  which  depends  upon  the 
absolute  temperature,  and  usually  increases  with  it, 
and  also  upon  the  nature  of  the  solvent. 

We  will  now  see  what  happens  when  a  metal,  with 
a  high  solution  tension,  Zn,  is  placed  in  a  solution  of 
one  of -its  salts,  ZnSO4.  The  pressure  Pis  here  much 
larger  than  /,  the  osmotic  pressure  of  the  Zn  ions 
in  the  solution,  and  so  the  Zn  plate  dissolves,  and 
Zn  ions  (+)  go  into  the  solution  from  it,  and  leave 
negative  electricity  on  the  plate.  According  to  the 
present  physical  theory,  all  neutral  substances  are 
charged  with  electricity,  both  positive  and  negative, 
but  in  equal  amounts;  and  so  if  we  remove  the  posi- 
tive, the  negative  remains  behind,  as  above.  This 
works  electrostatically  upon  the  positive  ions  in  the 
liquid,  and  in  that  way  diminishes  the  solution  tension. 
The  process  continues  until  equilibrium  is  reached 
between  the  solution  tension  and  the  electrostatic 
attraction,  when  it  ceases.  To  bring  about  this  state, 
however,  we  need  but  a  very  small  quantity  of  metal, 
for  the  electrical  charges  of  the  ions  are  enormous. 

We  have  now  the  following  state.  The  zinc  has  an 
amount  of  negative  electricity  upon  its  surface  which 
electrostatically  attracts  the  positive  ions  in  the  solu- 


4O  THE    THEORY  OF  SOLUTION. 

tion.  The  solution  has  an  excess  of  positive  ions  in 
it  and  is  consequently  positive.  Therefore  metals 
with  large  solution  tensions  in  solutions  of  their  salts 
form  always  the  negative  pole  of  the  cell,  t/*e  positive 
pole  being  tJie  solution.  The  negative  electricity  of 
the  metal,  attracting  the  positive  of  the  solution, 
forms  an  equilibrium  in  the  form  of  what  Helmholst 
calls  an  electrical  double  layer.  These,  according  to 
Helmholst,  always  form  whenever  two  conductors  of 
different  potential  come  together.  As  soon  as  the 
solution  and  metal  are  connected  outwardly,  this 
double  layer  is  broken  up  and  the  true  potential 
difference  of  the  two  bodies  is  shown;  on  breaking 
again  the  outward  connection,  the  double  layer  is 
formed  just  as  before.  Equilibrium  will  be  reached 
with  metals  of  this  kind  the  sooner,  the  smaller  the 
concentration  of  the  metal  ions  in  the  solution  is,  and 
the  potential  difference  will  be  the  greater. 

We  will  now  consider  a  metal  (Cu)  with  a  very  small 
solution  tension.  In  this  case  the  osmotic  pressure 
of  the  metal  ions  in  the  salt  solution  will  be  greater 
than  the  solution  pressure  of  the  metal,  and  so  metal 
ions  will  go  to  the  electrode  and  there  give  up  their 
positive  charges  and  become  metallic.  The  metal  in 
this  case  b.ecomes  charged  with  positive  electricity,  and 
equilibrium  will  be  reached  when  the  electrostatic 
repulsion  of  the  metal  ions  by  the  positive  plate 
becomes  equal  to  the  osmotic  pressure  of  the  ions  in 
solution.  With  metals  of  this  type  the  equilibrium 
will  become  established  the  sooner,  the  more  dilute 
the  solution  is,  and  the  potential  difference  will  be 
smaller.  (Contrast  with  the  first  case.) 


THE    THEORY  OF  THE    VOLTAIC  CELL.  4! 

According  to  the  conception  of  solution  tension, 
evejy  metal  should  show  a  certain  potential  in  a  solu- 
tion of  one  of  its  salts  (of  a  ceitain  concentration),  and 
this  we  find  to  be  a  fact.  It  also  holds  for  the  metals  in 
acids,  for  by  aid  of  the  oxygen  of  the  air  (which  can- 
not be  excluded)  traces  (at  any  rate)  of  metal  are  dis- 
solved, and  so  a  dilute  solution  formed,  which  acts 
just  as  any  other  solution.  Of  course  these  results 
are  not  so  constant,  for  the  element  of  chance  enters 
into  it,  as  far  as  the  amount  dissolved  is  concerned. 
What  small  amounts  of  metal  dissolved  will  give  these 
results  we  will  calculate  later. 

Nernst,  by  considering  these  two  pressures  (i.e., 
osmotic  and  solution)  just  as  we  would  gaseous  pres- 
sures, has  succeeded  in  working  out  a  formula  for 
each  electrode,  giving  just  the  E.M.F.  that  is  pro- 
duced.* The  formula  for  each  single  electrode  is 


7fl  =  cog  ~t      7t^  =         og~, 
P\  Pi 

and  the  total  E.M.F.  of  a  cell  made  up  of  two  such 
electrodes  is 


0.0002W,     . 

where  c    is  a  constant  =  —      -  (nt  =  valence  of 


*  He  assumes  that  an  electric  cell  is  a  machine  run  by  dif- 
ferences of  pressure,  and  all  his  assumptions  have  been  proven 
correct,  as  have  the  formulae.  For  details  see  Zeit.  f.  Phys. 
Chem.,  IV.  149  (1889). 


42  THE    THEORY  OF  SOLUTION. 

metal,  and  nl  the  number  of  the  ions  of  that  kind  pro- 
duced by  the  dissociation  of  one  molecule),  T  is  the 
absolute  temperature,  P1  and  /*  are  the  two  solution 
pressures,  and  pl  and  p^  the  corresponding  osmotic 
pressures.  7/j  and  nt  are  the  differences  of  potential 
caused  by  contact  of  the  two  liquids  and  the  two 
metals;  these,  however,  we  can  neglect.  Although  it 
is  not  possible  for  us  here  to  follow  the  mathematical 
development  of  the  formula,  still  we  will  probably  be 
able  from  the  sketch  of  the  process  to  understand  it. 
The  constant  c  (whose  value  is  given  above)  is  simply  a 
constant  which  causes  the  results  to  be  given  in  volts. 
By  the  aid  of  the  formula  given  for  each  separate 
electrode, 

P 
Tr^cTlog-1, 

it  has  been  possible  to  calculate  the  different  values 
of  P  in  atmospheres.  The  values  vary  greatly ;  some 
are  enormous,  others  very  small,  n  in  the  formula  is 
the  potential  of  the  metal  against  a  normal  (i  liter) 
solution  of  one  of  its  salts,  /,  being  the  osmotic  pres- 
sure of  the  metal  ions  of  the  solution,  i.e.,  a  X  22.32 
atmospheres,*  for  if  entirely  dissociated,  the  ion  con- 
sidered would  have  a  pressure  of  22.32  atmospheres. 

Metals.  Symbol.      P  (atmospheres). 

Zinc Zn  2.7x10" 

Cadmium Cd  7-4  X  io6 

Thallium Tl  2.1  X  io3 

Iron   Fe  3.2X10* 

*  Neumann,  Zeit.  f.  Phys.  Chem.,  XIV.  223. 


THE    THEORY  OF   THE    VOLTAIC  CELL.  43 

Cobalt Co  5.2  X  10° 

Nickel Ni  3.5X10° 

Lead Pb  3.1  X  io~ 

Hydrogen H  2.7  X  10 

Copper Cu  1.3  X  10 

Mercury , Hg  3.iXiO~18 

Silver Ag  6.4  X  IO~17 

Palladium Pd  4.0  X  10 


_3 
-19 


-36 


These  metals  are  arranged  in  the  order  of  the  old 
contact  series  (Volta)  for  air,  and  with  one  or  two 
exceptions  it  seems  to  be  also  the  proper  one  for 
solutions.  We  must  remember  the  greater  the  solu  - 
tion  pressure  is  the  more  negative  a  metal  will  be  as 
against  its  solution. 

In  a  Daniell  cell  the  E.M.F.  is  1.06  volts;  here  the 
osmotic  pressures  are  insignificant  as  compared  with 
the  solution  pressures;  thus  in  our  formula  (Pl  =  Zn, 
P.  =  Cu) 


we  can  cause  /,  and  p^  to  be  the  same,  and  so  they 
disappear  and  our  formula  becomes 


or 


log  /in  =   36.  $/>Cu,        Or       PZn  =    10*5/>C« 


44  THE    THEORY  OF  SOLUTION. 

According  to  our  results,  as  found  experimentally  for 
the  single  electrodes  (see  table),  we  have 


which  can  be  looked  upon  as  a  very  good  agreement, 
considering  all  the  circumstances,  and  goes  to  prove 
that  our  theory  of  a  cell  is  the  correct  one. 

We  are  now  in  position  to  calculate  the  amounts  of 
metal  ions  in  a  solution  which  are  necessary  to  give  a 
potential  in  connection  with  the  metal.  This  is  for 
the  case  of  metals  in  acids  in  which  they  are  not  solu- 
ble, spoken  of  before.  We  will  assume  that  PCu  = 
io~l8  atmospheres  (which  is  certainly  too  large).  A 
solution  of  a  copper  salt  at  20  liters  dilution  has  an 
osmotic  pressure  of  Cu  ions  of  one  atmosphere.  To 
have  a  solution  with  a  pressure  of  io~  l8  atmospheres 
it  is  only  necessary  to  take  the  2O  X  IO"  l8  part  of  a 
mol;  and  this  would  still  be  greater  than  the  solution 
pressure  of  the  metal,  and  so  give  a  potential  differ- 
ence. The  amount  of  Cu  (20  X  io~  l8  mol),  however, 
is  so  small  that  we  cannot  detect  it  analytically  by 
any  known  method,  and  it  approaches  in  size  a  mole- 
cule. According  to  the  latest  measurements  in  one 
mol  there  are,  in  round  numbers,  5  X  io23  atoms,  i.e., 
in  one  liter  of  the  above  solution  there  are  about 
25,000;  so  that  in  one  cubic  centimeter  25  atoms 
suffice  to  cause  such  a  pressure  that  the  copoer  in  its 
solution  has  a  potential  of  zero. 

There  is  a  certain  type  of  cell  which  was  impossible 
to  understand  by  the  old  theory,  for  no  chemical 
action  takes  place  in  it;  but  by  the  new  theory,  as  we 
have  sketched  it,  it  becomes  very  simple.  I  refer  to 


THE    THEORY  OF   THE    VOLT^TC~CE'LL.  45 


concentration  cells,  i.e.,  where  the  same  metal  is  used 
on  both  sides  as  electrodes,  and  the  solutions  are  the 
same  substance  but  of  different  concentration.  An 
example  of  this  is 


which  gives  an   electromotive  force  of  o.  116  volts,  or 

Ag  |  AgNO,TVN-KN03-KAgCN,TVN  |  Ag. 
E.M.F.  (TT)  =1.14  volts. 

The  KNO3  is  used  as  a  connecting  link  in  the  first, 
to  remove  any  E.M.F.  that  would  arise  by  contact  of 
the  two  liquids;  and  in  the  second  for  the  same  reason, 
and  also  because  the  two  salts  form  a  precipitate  when 
they  come  in  contact.  In  cases  like  the  first,  how- 
ever, the  KNO3  is  not  necessary  if  we  make  allowance 
for  the  E.M.F.  generated  by  the  contact  of  the  two 
solutions  in  the  formula,  as  Nernst  has  done.  The 
experimental  .and  the  theoretical  results  obtained  by 
him  were  found  then  to  agree  very  well.  For  our 
purpose,  however,  simplicity  is  important,  so  we  will 
use  the  KNO3.  According  to  our  earlier  considera- 
tions the  E.M.F.  of  such  a  combination  will  be 
expressed  by  the  formula 

7t  nr  C  T  \  log log  ~" 

Pl  and  P^  ~  solution  pressure  for  silver,  which  is  con- 
stant for  same  solvent  and  temperature,  and  hence  Pl 
and  Pn  cancel.  Our  formula  is  then 


46  THE    THEORY  OF  SOLUTION. 

where  /a  is  the  osmotic  pressure  on  the  more  concen- 
trated side,  and  /,  that  on  the  other. 

Silver  has  a  negative  solution  pressure,  and  so  ions 
of  silver  will  leave  the  solution  and  discharge  on  the 
electrodes.  This  will  happen  on  both  sides,  but  with 
a  different  pressure  of  silver  ions  on  the  two  sides. 
Thus  both  silver  electrodes  are  positive,  but  the  one 
on  the  concentrated  side  is  more  positive  than  the 
other,  and  so  it  will  be  our  positive  pole;  i.e.,  elec- 
tricity (-f)  will  go  from  the  concentrated  side  through 
a  wire  to  the  other.  A  contrary-directed  current  of 
negative  electricity  will  go  through  the  liquid  to  the 
concentrated  side.  As  soon  as  Ag  ions  have  been 
precipitated  upon  the  concentrated  side  their  elec- 
tricity will  drive  silver  ions  out  on  the  other,  and  this 
action  will  continue  until  the  two  solutions  are  of  the 
same  concentration,  when  it  will  cease. 

There  is  another  type  of  cell  differing  in  action 
apparently  from  any  we  have  as  yet  considered ;  it  is 
the  so-called  oxidation  and  reduction  *  element.  In 
principle  it  is  very  simple,  and  may  be  thoroughly 
understood  from  the  following  typical  example:  If  we 
have  a  Pt  electrode  (coated  with  platinum  black)  in  a 
solution  of  stannous  chloride  on  the  one  side,  and 
another  in  a  solution  of  ferric  chloride  on  the  other, 
and  connect  the  two  with  a  wirr,  a  current  of  elec- 
tricity passes  from  the  one  on  the  iron  side,  through 
the  wire  to  the  one  in  the  J£n  solution, f  and  vice 
versa  through  the  solution.  The  iron  ions  (•••)  on 

*  Bancroft,  Zeit.  f.  Phys.  Chem. 

f  Of  course  to  get  a  current  it  is  also  necessary  to  connect  the 
two  solutions  with  a  siphon. 


VOLT  A. 


THE    THEORY  OF   THE    VOLTAIC  CELL.  4/ 

the  one  side  strive  to  get  into  the  divalent  form,  and 
so  give  up  one  equivalent  of  electricity  to  the  elec- 
trode, and  this  goes  to  the  other  electrode  (through 
the  wire)  and  allows  the  tin  ions  (••)  to  get  into  the 
tetravalent  state  (by  absorbing  electricity).  The 
action  is  thus  one  of  oxidation  on  the  one  side  and 
reduction  on  the  other.  The  above  action  of  course 
only  takes  place  when  the  electricity  given  up  by  the 
iron  ions  (Fe***  to  Fe"),  can  be  used  by  the  Sn  ion 
(Sir-  to  Sir---). 

We  have  a  true  oxidation  when  negative  electricity 
is  formed  on  an  ion,  or  when  positive  is  given  up  by 
an  ion.  A  reduction  is  naturally  the  opposite  to 
this;  that  is,  when  positive  electricity  is  formed  on  an 
ion,  or  when  negative  is  given  up.  If  only  negative 
ions  are  given  up,  then  the  process  is  one  of  oxidation. 
All  solutions,  however,  can  cause  either  oxidation  or 
reduction  (according  as  the  -f-  or  —  ions  disappear  or 
are  formed),  for  in  them  there  are  present  equal 
amounts  of  positive  and  negative  ions. 

From  the  above  it  is  apparent  that  the  process  in 
cells  of  this  type  does  not  differ  so  widely  from  that 
of  the  Danieli.  In  the  latter  case  the  reduction  takes 
place  at  the  zinc  electrode,  the  oxidation  at  the 
copper.  But  this  is  simply  a  case  of  two  reductions 
where  the  one  (Zn)  is  greater  than  the  other,  for  all 
metals  give  out  only  positive  ions,  but  to  different 
pressures,  and  this  difference  causes  the  current. 

DISSOCIATION  BY  AID  OF  THE  E.M.F. 

Before  closing  this  chapter  with  a  brief  account  of 
the  processes  taking  place  in  practical  and  storage 


48  THE    THEOR  Y  OF  SOL  U  TION. 

batteries,  it  will  be  well  to  consider  the  method  of 
Ostwald's,  mentioned  before,  of  determining  concen- 
tration of  metal  ions  by  aid  of  the  E.M.F.  As 
osmotic  pressure  is  proportional  to  concentration,  we 

can  substitute  for  —  '  their  values  -^  in  the  equation 


and  we  get 

n=cT\og$*. 

C9  (mols  per  liter)  of  solution  on  the  positive  side,  Cl 
that  on  the  other.  If  we  know  £*„  TT,,  T,  and  C,  we 
can  find  Ct. 


This  formula  was  used  first  by  Ostwald  for  the  cell 
with  AgNO,f\  and  KAgCuafvff,  n  =  1.14  volts,  log 
C,  =  --  i,  T—  273°  +  17°  =  290°;  hence 

*      *  ~  .0002  X  290' 

log  C,  =  --  i  —  19.6  =  —  20.6, 
Cv  =  io-20-6. 

That  is,  there  are  108  grams  (one  mol)  of  silver  ions  in 
io20-6  liters  of  T^KAgCua.  This  amount  is  so  small 
as  not  to  be  shown  by  any  analytical  method,  for  a 
reason  to  be  given  later.  But  just  here  is  the  value 
of  the  method,  for  the  smaller  the  number  of  Ag  ions 
present  the  larger  the  E.M.F.  is,  and  so  the  greater  the 


THE    THEORY  OF   THE    VOLTAIC  CELL.  49 

accuracy.  This  method  can  be  used  for  all  metals 
forming  good  constant  electrodes,  but  unfortunately 
that  number  is  not  large.  This  is  the  method  as  used 
by  the  author  to  determine  CN  ions  (Chap.  I). 

PRACTICAL  PRIMARY  AND  SECONDARY  BATTERIES.* 

By  the  aid  of  the  knowledge  we  have  gained  by  our 
consideration  of  the  voltaic  call  (that  is,  the  relations 
of  the  osmotic  pressure  of  the  ions  to  the  solution 
pressure  of  the  metals)  we  are  now  in  position  to  dis- 
cuss and  understand  the  practical  batteries  with  which 
we  come  in  contact  every  day.  Of  course  in  practice 
the  concentration  cells  are  of  but  little  use  to  us,  for 
their  age  is  too  short,  i.e.,  the  concentrations  become 
equalized  very  rapidly,  and  so  the  current  soon  ceases 
to  flow.  Still  a  knowledge  of  them  in  connection  with 
one  of  solution  pressure  is  of  great  value  to  us,  for  in 
them,  as  in  all  other  batteries,  the  process  depends 
upon  the  same  factors. 

The  process  taking  place  in  the  Daniell  cell,  as  has 
already  been  mentioned,  consists  of  formation  of  ions 
of  Zn  and  the  disappearance  of  an  equal  number  of 
those  of  Cu,  caused  by  the  great  difference  of  the  solu- 
tion pressures  of  Zn  and  Cu.  We  will  now  consider 
another  constant  cell,  i.e.,  one  giving  a  constant 
E.M.F. 

The  Clark  standard  cell  consists  of  Zn  in  a  solution 
of  ZnSO4  and  Hg  covered  with  a  paste  of  Hg2SO4. 

*  In  this  chapter  Le  Blanc's  Lehrbuch  der  Elektrochemie  has 
been  freely  used. 


SO  THE    THEORY  OF  SOLUTION. 

This  Hg3SO4  is  insoluble,  but,  as  will  be  seen  in  the 
next  chapter,  all  salts  are  soluble  to  a  certain  extent 
(even  though  it  be  very  small),  and  so  we  can  assume 
that  there  are  HgHg  and  SO4  ions  present.  The 
process  then  is  the  following:  Positive  Zn  ions  are 
forced  (by  solution  pressure)  into  the  solution,  and 
these  go  through  the  solution  and  drive  (by  electro- 
static repulsion)  the  Hg  ions  out  to  the  electrode,  where 
they  give  up  their  charges  and  assume  the  metallic 
form.  Thus  the  Zn  losing  positive  electricity  (with 
the  ions)  is  the  negative  pole;  while  the  Hg  receiving 
positive  charges  from  the  ions  is  the  positive  one. 
That  is,  the  current  goes  through  the  wire  from  Hg 
to  Zn,  while  in  the  liquid  it  goes  from  Zn  to  Hg. 

The  Daniell  cell  is  more  valuable  for  giving  a  cur- 
rent than  the  Clark,  but  for  simply  a  known  constant 
E.M.F.  the  latter  has  the  advantage.  The  tempera- 
ture coefficient  (increase  of  E.M.F.  for  i°  C.)  is, 
however,  large  in  both;  but  that  is  true  of  all  elements 
using  saturated  solutions.  Of  course,  as  there  are  but 
few  ions  of  Hg  present  in  the  Clark,  they  are  soon 
used  up,  if  the  current  is  allowed  to  flow  (unless 
through  a  large  resistance),  and  then  the  E.M.F.  falls;. 
but  the  cell  recovers  on  standing,  as  then  more  ions 
of  Hg  are  given  off  by  the  Hg2SO4.  This  is  not  such 
a  great  disadvantage,  for  the  Clark  cell  is  used  as  a 
standard  for  the  E.M.F.,  and  always  has  a  compen- 
sating E.M.F.  against  it,  and  so  does  not  become  used 
up.  To  this  type  of  cell  belong  also  those  of  the 
Helmholst  and  Weston  pattern ;  and  their  action  is 
very  similar. 

To  the  type  of  inconstant  cells  belong  all  those  from 


THE    THEORY  OF   THE    VOLTAIC  CELL.  5 1 

which  we  obtain  large  amounts  of  electricity  at  a  large 
E.M.F.,  and  where  the  latter  is  not  required  to  be 
constant. 

The  Leclanche  cell  consists  of  a  solution  of  ammo- 
nium chloride  in  which  are  placed  the  two  electrodes 
Zn  and  carbon  -|-  MnO2  (manganese  dioxide).  Here 
we  have  to  distinguish  between  the  action  of  the  car- 
bon alone  and  the  carbon  -\-  MnO2.  First  we  will 
assume  Zn  and  carbon  alone  as  electrodes,  and  see 
what  disadvantages  the  cell  has;  then  we  will  bring 
the  MnO2  into  play,  and  see  how  it  changes  the  reac- 
tion and  removes  the  disadvantages.  If  the  elec- 
trodes of  the  cell 

Zn  -  NH4C1  -  C, 

are  connected,  the  Zn  ions  will  go  into  solution  (great 
solution  pressure  of  Zn),  and  hydrogen  gas  be  given 
off  at  the  C  pole.  The  zinc  ions  go  through  the  solu- 
tion and,  being  positive,  act  electrostatically  upon 
those  of  NH4,  driving  them  toward  the  carbon.  Here 
a  storing  up  of  an  excess  of  positive  ions  takes  place, 
and  as  H  ions  give  up  their  electricity  more  easily 
than  NH4  ions,  H  gas  collects  on  the  carbon,  and  it 

receives  the  electricity.      The  NH4  ions  then  form  an 

i 

equilibrium  with  those  of  OH.  The  Zn  electrode  is 
the  negative  pole,  having  lost  positive  electricity,  and 
the  C  the  positive  one,  having  received  the  -f-  charges 
from  the  H  ions.  The  hydrogen  gas  is  absorbed  by 
the  carbon  plate  and  then  given  off  in  the  air;  but 
this  giving  off  of  hydrogen  gas  is  not  rapid  enough, 
and  the  plate  becomes  saturated  with  it  and  so  pre- 
vents, partly,  other  ions  from  discharging  to  it,  and  in 
consequence  the  E.M.F,  falls  rapidly.  In  order  to 


52  THE    THEORY  OF  SOLUTION 

get  rid  of  this  objection  the  MnO3  is  used.  With  it, 
however,  the  action  is  entirely  changed,  and  now  goes 
as  follows:  We  know  that  every  substance  is  soluble 
to  a  certain  extent  (Chap.  IV),  even  though  it  be  very 
small,  so  we  know  that  there  are  ions  of  Mn  present. 
The  reaction  is 

MnO,  +  2HaO  =  Mn  +  4OH. 

These  tetravalent  ions  of  Mn  have  the  tendency,  as 
before  remarked,  to  give  up  two  equivalents  of  elec- 
tricity and  to  assume  the  form  of  divalent  ions,  Mri. 
In  consequence  of  this  the  zinc  ions  go  through  the 
solution  as  before,  but  this  time  drive  the  Mn  ions  to 
the  electrode,  where  they  give  up  the  two  equivalents 
of  electricity  (more  easily  even  than  do  those  of  H) 
and  become 

MnCl,(Mn  +  2Cl). 

This  action  takes  place  evenly,  until  the  concentration 
of  Zn  ions  in  the  solution  becomes  so  great  that  no 
more  can  be  formed  by  the  Zn;  then  the  E.M.F.  falls. 
New  NH4C1  solution,  however,  renews  the  action. 

The  other  primary  element  of  this  type  that  we  will 
discuss  is  the  combination 

Zn  -  H,SO4  +  K2Cr2O7  -  C. 

At  the  negative  electrode  here  Zn  ions  are  also  driven 
into  the  solution;  at  the  positive  pole  (C),  however, 
the  action  is  more  complicated.  The  action  of  H,SO4 


THE    THEORY  OF  THE    VOLTAIC  CELL.  53 

upon  K2Cr2O7  is  practically  to  form  chromic  acid 
(H2CrO4) ;  this,  however,  dissociates  to  a  large  degree 
into 

HHa+CrO4. 

As  we  know,  substances  which  dissociate  in  this  way 
usually  dissociate  further,  to  a  slight  degree,  into 
metal  ions  (Chap.  I);  this  is  the  case  with  chromic 
acid. 

H3CrO4  +  2HaO  =  Cr  +  6OH. 

These  hexavalent  Cr  ions  have  the  tendency  to  give 
up  three  equivalents  of  electricity  and  assume  the 
trivalentjorm  Cr*".  Accordingly  the  zinc  ions  (just 

as  before  with  the  Mn"**)  drive  the  Cr ions  to  the 

electrode,  where  they  give  up  three  equivalents  and 
become  Cr*",  in  equilibrium  SO4  as  Cr2(SO4)3.  This 
is  what  happens  in  all  cases  when,  in  a  cell,  the  valence 
of  an  element  changes,  for  they  give  up  their  extra 
equivalents  much  more  readily  than  any  element  could 
give  up  its  entire  charge. 

Accumulators,  Storage  or  Secondary  Batteries. — A 
cell  of  this  description  is  any  one  in  which  electrical 
energy  can  be  stored  up  in  the  form  of  chemical 
energy,  and  used  as  required.  All  reversible  *  cells 
can  be  used  as  storage  batteries  by  passing  a  current 
through  them,  so  that  the  reaction  goes  in  the 
opposite  direction  from  which  it  goes  in  the  cell. 
Thus  a  Daniell  element  which  has  been  used  up 

*  A  reversible  cell  is  one  in  which  all  the  products  of  the  reac- 
tion still  stay  in  accessible  form  in  the  cell.  If  a  gas  is  formed, 
the  cell  is  not  reversible. 


54  THE   THEORY  OF  SOLUTION. 

(i.e.,  when  so  much  zinc  has  been  dissolved  as  to 
prevent  further  formation  of  Zn  ions)  can  be  regen- 
erated by  passing  a  (-(-)  current  through  the  Cu,  and 
so  on  through  the  liquid  to  the  Zn ;  this  sends  Cu  ions 
into  solution,  and  precipitates  the  Zn  ions  upon  the 
Zn  as  metal.  The  element  is  thus  brought  into  its 
original  state  again  and  can  be  used  once  more.  Thus 
we  have 

Zn  +  Cu  +  SO4  X  Zn  +  SO4  +  Cu. 

The  left  side  represents  the  cell  when  ready  for  use, 
the  right  when  used  up. 

The  lead  accumulator  is,  however,  the  one  generally 
used.  It  consists  before  being  charged  of  two  lead 
plates,  one  being  coated  with  litharge  (PbO)  in  a  20$ 
solution  of  sulphuric  acid.  If  now  we  pass  a  current 
of  electricity  through  this  (PbO  on  -j-  pole),  superoxide 
of  lead  (or  supersulphate)  is  formed  on  the  PbO  side 
and  spongy  lead  on  the  negative  one.  The  cell  when 
fully  charged  is  then  an  element  with  PbOa  and  Pb  as 
electrodes  in  sulphuric-acid  solution.  By  discharging 
the  reaction  is 

PbOa  +  2H2SO4Aq  +  Pb  =  2PbSO4  +  Aq  +  8;oK. 

that  is,  the  PbOa  and  the  Pb  are  transformed  into 
PbSO4.  According  to  this  reaction  the  E.M.F. 
should  be  1.9  volts  at  o° ;  the  higher  potentials  are 
caused  by  the  positive  temperature  coefficient,  i.e., 
where  the  potential  one  increases  with  increased  tem- 
perature. Now  for  the  process  that  takes  place  on 


THE    THEORY  OF  THE    VOLTAIC  CELL.  55 

discharging.  The  PbO2  is  soluble  to  a  slight  extent, 
and  with  water  dissociates  as  follows: 

PbO,  +  2H2O  =  Pb-  —  +  4OH. 

These  tetravalent  Pb  ions  have,  however,  the  ten- 
dency to  give  up  two  of  their  equivalents  of  electricity 
and  to  go  into  the  state  Pb".  From  the  lead  plate, 
when  the  two  are  connected,  ions  of  lead  are  given  up 
and  drive  the  Pb —  ions  electrostatically  to  the  PbO, 
plate,  where  they  lose  their  two  charges  and  become 
PbSO4.  From  the  lead  plate  the  pressure  of  Pb  ions 
is  greater  than  from  the  other,  and  so  the  former  drive 
those  of  the  latter  through  the  solution.  The  PbO 
plate  is  thus  positive,  against  the  one  of  Pb. 

According  to  Le  Blanc  the  principal  source  of  the 
E.M.F.  of  this  cell  is  the  change  of  valence  from  Pb — 
to  Pb-. 

The  tetravalent  ions  of  Pb  as  they  are  used  up  are 
supplied  by  the  PbO2  plate.  The  Pb"  ions  from  the 
negative  plate  go  into  solution  and  form  PbSO4,  but 
the  formation  of  this  has  but  little  influence  upon 
the  E.M.F. 

So  much  for  the  theory  of  this  cell;  the  explanation 
of  its  irregularities  and  certain  others  of  its  character- 
istic actions  can  be  found  in  Dr.  Le  Blanc's  book.* 
We  will  only  add  here  that  all  the  processes  have  been 
made  clear,  and  are  described  in  full,  with  reference 
to  our  theory,  in  the  above  work. 


*  See  Preface. 


CHAPTER    IV. 

ANALYTICAL  CHEMISTRY  FROM  THE  STANDPOINT 
OF   ELECTROLYTIC   DISSOCIATION. 

THIS  subject  has  been  so  thoroughly  treated  by 
Ostwald  that  here  only  enough  will  be  given  to  show 
what  great  value  our  theory  possesses  in  this  branch, 
as  well  as  in  the  treatment  of  electrical  elements. 
Those  wishing  to  follow  the  subject  into  its  details 
are  referred  to  Ostwald's  book.* 

Analytical  chemistry  has  always  been  an  empirical 
science,  i.e.,  we  know  that  certain  things  occur  under 
certain  conditions,  but  do  not  know  why  they  do  so. 
Ostwald  has,  however,  succeeded  in  removing  the 
greater  part  of  this  difficulty  by  the  aid  of  the  theory 
of  electrolytic  dissociation. 

We  found  in  Chapter  I  that  the  ions  are  the  active 
parts  in  a  chemical  reaction,  and  that  when  they  are 
present  they  give  well-known  reactions,  but  not  when 
the  element  is  a  part  of  a  complex  ion.  According 
to  this,  then,  we  must  always  consider  in  reactions  the 
ions  and  their  quantity,  rather  than  the  substances 
themselves. 

When  a  substance  dissociates  there  is  a  certain  rela- 
tion between  the  dissociated  and  undissociated  parts 

*  Scientific  Aspects  of  Analytical  Chemistry.  Trans,  by 
McGowan.  (Macmillan,  1895.) 

56 


ANALYTICAL    CHEMISTRY.  57 

which  is  expressed  for  a  substance  which  falls  into 
two  ions  by  the  formula 

c,d,  =  KC, 

I 

where  Ct  is  the  kathion  (•)  and  Ca  ()  is  the  anion,  C 
the  concentration  of  undissociated  portion,  and  K  the 
dissociation  product.  This  is  also  expressed  (Chap. 
II)  by 


where  a  =  degree  of  dissociation,  and  v  =  dilution 
(number  of  liters  in  which  i  mol  is  dissolved).  Thus 
for  large  v,  a  is  also  large.  For  the  neutral  salts  K  is 
very  large,  and  differs  for  the  different  ones  but 
slightly,  while  for  acids  it  is  small,  and  is  greater  or 
smaller  according  as  the  acid  is  strong  or  weak.  This 
difference  becomes  smaller,  the  weaker  the  solution; 
for  an  infinite  dilution,  all  would  be  equally  strong, 
for  all  would  be  completely  dissociated. 

All  substances  are  soluble  to  a  certain  extent  even 
though  it  be  very  small,  and  this  part  in  solution  we 
can  assume  without  error  to  be  very  largely  dissoci- 
ated. Nernst  *  has  proved  the  following  two  laws: 

I.  In  a   saturated  solution  of  a  partly  dissociated 
substance,  the  active  mass  of  the  undissociated  portion 
remains   constant    under   all  conditions,  even    when  a 
second  substance  is  added.  • 

II.  The  product    of  the   active   masses  of  the  ions 

*Zeit.  f.  Phys.  Chem.,  IV.  372  (1889). 


$8  THE    THEORY  OF  SOLUTION. 

formed  by  the  dissociation  also  remains  constant,  when 
the  solution  is  saturated. 

The  task  for  the  analytical  chemist  is  then  to  make 
this  dissociated  part  as  small  as  possible.  This  is 
accomplished  by  adding  another  substance  with  an  ion 
in  common,  thus  driving  the  dissociated  portion  back 
into  the  undissociated  portion.  The  solution,  how- 
ever, is  already  saturated  with  this,  and  when  more  is 
formed  it  is  precipitated  out  as  insoluble. 

For  elements  or  indifferent  substances  there  is  no 
way  to  do  this  but  by  lowered  temperature,  or  by 
adding  some  other  solvent  in  which  the  solubility  is 
less;  these  cases,  however,  we  will  leave  out  of  con- 
sideration, for  they  are  neither  numerous  nor  of  much 
importance. 

In  a  saturated  solution  we  have  a  complex  equi- 
librium between,  first,  the  solid  body  and  the  undis- 
sociated part  (small)  in  solution;  second,  this  undisso- 
ciated part  in  solution  and  the  ions  of  the  same. 

The  first,  however,  by  the  first  law  of  Nernst, 
remains  constant.  For  the  second  case  we  have,  for 
binary  electrolytes, 

C,C2  =  KC. 

Since  C,  as  we  have  just  found,  is  constant  (for  a  cer- 
tain temperature)  in  saturated  solutions,  therefore  KC 
is  also,  and  also  C,Ca.  Thus  for  equilibrium  between 
a  precipitate  and  its  solution  the  product  of  the  con- 
centrations of  its  ions  (C,  and  C,)  must  reach  a  certain 
value;  this  value  is  called  the  solubility  product.  From 
another  standpoint  it  means  this:  tJiat  a  precipitate 
can  form  only  when  the  product  of  the  concentrations  of 


ANALYTICAL   CHEMISTRY.  59 

the  ions  (£7,  and  Cy)  has  reached  a  certain  value.  This 
follows  simply  from  the  above,  for  it  is  the  condition 
of  equilibrium  between  a  solid  and  a  solution;  and  no 
precipitate  can  form  without  equilibrium,  for  in  that 
•case  it  would  immediately  redissolve. 

In  analytical  chemistry  the  object  is  to  separate  one 
element  in  insoluble  form,  and  then  to  weigh  it.  Let 
us  take  for  example  the  case  of  the  determination  of 
SO4  with  BaCl3.  If  we  add  just  enough  Ba  salt,  then 
some  SO4  ions  will  remain  free,  but  not  enough  with 
the  Ba  ions  present  to  reach  in  value  the  solubility 
product  of  BaSO4.  This  amount  can,  however,  be 
made  insignificant  by  adding  more  Ba  salt,  for  the 
greater  the  concentration  of  that  is,  the  smaller  will 
be  the'  amount  of  SO4  ions  necessary  to  reach  in  value 
the  solubility  product.  Still  the  amount  of  SO4  ions 
can  never  be  made  zero,  for  that  of  the  Ba  ions  can 
never  be  made  infinite;  but  the  amount  is  so  small 
that  even  if  we  did  precipitate  it  we  could  not  find  any 
difference  in  our  two  weights. 

This  was  long  ago  discovered  practically,  when  it 
was  found  best  always  to  add  an  excess  of  the  precipi- 
tate; but  for  its  scientific  explanation  Ostwald  must 
receive  the  credit.  Of  course  the  more  soluble  the 
precipitate  the  greater  must  be  the  excess  of  the  pre- 
cipitant. For  to  decrease  the  solubility  to  \/n  of 
what  it  is  in  pure  water,  it  is  necessary  to  add  n  times 
the  amount  of  the  other  ion.  A  small  excess,  how- 
ever, is  all  that  is  necessary  in  practice,  for  all  the  pre- 
cipitates used  are  very  insoluble,  and  so  have  of  them- 
selves a  very  small  solubility  constant. 

All  this  holds  also  in  washing  our  precipitates;  thus 


60  THE    THEORY  OF  SOLUTION. 

we  often  use  water  containing  one  of  the  ions  of  the 
solid,  in  order  to  keep  it  insoluble.  For  example,  we 
wash  lead  sulphate  with  a  dilute  solution  of  sulphuric 
acid,  and  mercurous  chromate  with  mercurous  nitrate; 
but  of  course  we  must  use  those  substances  which  can 
be  removed  most  easily,  so  as  not  to  interfere  with  the 
other  operations. 

It  is  perhaps  confusing  to  think  fhat  the  ions  are 
the  active  members  of  a  chemical  equation ;  for  then 
it  would  seem  that  we  would  get  only  such  an  amount 
of  precipitate  as  corresponds  to  the  number  of  ions 
present.  A  minute's  thought,  however,  will  clear 
away  all  doubt,  and  show  that  all  the  substance  pres- 
ent enters  into  the  reaction.  If  we  have  a  solution 
which  is  10$  dissociated  into  two  ions,  and  we  add  a 
substance  in  such  an  amount  as  just  to  combine  with 
all  these  ions  and  form  an  insoluble  compound,  then 
it  is  natural  to  think  that  a  further  addition  will  pro- 
duce no  more  of  the  precipitate,  for  we  have  used  up 
all  the  ions.  But  we  forget  that  as  soon  as  those  ions 
disappear,  more  of  the  salt  must  dissociate  until  the 
pressure  of  the  ions  is  the  same  as  before;  then  an 
addition  of  the  precipitate  will  combine  with  these, 
and  the  process  will  go  on  until  all  the  salt  has  been 
dissociated  by  steps. 

The  solubility  product  explains  why,  in  cases  where 
we  know  ions  to  be  present  to  a  very  small  amount, 
we  cannot  prove  their  presence  by  analytical  means, 
for  their  concentration  is  so  small  that  almost  an  in- 
finite amount  of  the  ions  of  the  precipitant  would 
have  to  be  added  before  the  solubility  product  could 
be  reached. 


ANALYTICAL    CHEMISTRY.  6 1 

As  we  have  seen,  the  neutral  salts  are  always  more 
completely  dissociated  than  the  corresponding  acids. 
This  is  well  shown  by  the  fact  that  calcium  salts  are 
precipitated  by  all  carbonates,  but  free  carbonic  acid 
has  no  action  upon  them.  Carbonic  acid  in  water  is 
but  slightly  dissociated  into  ions,  and  so  the  product 
of  the  concentration  of  CO3  ions,  and  that  of  the  Ca 
ions  (even  though  present  in  large  amounts)  does  not 
attain  the  value  of  the  solubility  product  of  CaCO3. 

With  regard  to  lead  salts  this  is  somewhat  different. 
Lead  carbonate  is  more  insoluble  than  calcium  car- 
bonate and  so  the  product  is  smaller,  and  so  is  reached 
with  a  solution  of  carbonic  acid  and  a  precipitate 
forms.  This  precipitate  is,  however,  but  a  portion  of 
the  total  amount  of  lead  present.  Carbonic  acid  in 
wate.r  dissociates  to  a  small  extent  into  HH  and  CO3. 
If  we  use  lead  nitrate,  the  Pb  ions  disappear  from  the 
solution,  and  more  are  formed  and  finally  an  equilib- 
rium is  established  between  the  H  ions  of  the  car- 
bonic acid  and  the  NO3  of  the  Pb(NO3)2;  these  H 
ions,  however,  act  upon  those  «of  the  carbonic  acid, 
sending  them  back  into  the  undissociated  portion,  and 
of  course  the  CO3  ions  go  with  them,  and  so  no  more 
PbCO3  is  formed.  This  takes  place  with  Pb(NO3) 
after  a  very  small  amount  of  PbCO3  has  been  formed; 
because  HNO8  is  a  strong  acid  and  very  largely  dis- 
sociated. With  lead  acetate,  however,  it  takes  place 
after  it  is  two  thirds  decomposed,  for  acetic  acid  is  but 
little  dissociated,  and  so  much  more  of  it  must  be 
formed  before  the  osmotic  pressure  of  H  ions  is  as 
great  as  in  the  case  of  IINO3  (at  the  end  of  the  reac- 
tion). 


62  THE    THEORY   OF  SOLUTION. 

In  exactly  the  same  way  most  of  the  reactions  of 
analytical  chemistry  can  be  explained.  Those  that 
have  been  given,  however,  show  the  influence  of  the 
theory  upon  analytical  chemistry*  as  well  as  a  large 
number  would ;  and  so  we  will  close  with  a  few  con- 
siderations concerning  indicators  for  volumetric  analy- 
sis, which  will  explain  their  behavior  and  help  to 
retain  their  applicability  in  our  minds. 

INDICATOR  FOR  VOLUMETRIC  ANALYSIS. 

Under  this  head  we  will  consider  only  those  used 
in  acidimetry  and  alkalimetry.  An  indicator  is  a  sub- 
stance which  possesses  a  different  color  when  in  acid 
and  alkaline  solutions.  They  are  either  acids  or  bases 
and  are  but  very  slightly  dissociated,  the  less  so  the 
more  accurate  they  are. 

Phcnolplithalcin  is  a  weak  acid  indicator,  whose 
molecule  is  colorless  and  whose  ion  is  an  intense  red 
It  dissociates  into  H  and  the  ion  of  the  complex  radicle, 
which  is  red.  If  added  to  an  acid,  the  large  number 
of  H  ions  of  the  acid  drive  those  of  the  indicator 
back,  forming  the  colorless  undissociated  molecule. 
If  added  to  a  base,  then  water  and  a  salt  are  formed; 
but,  as  we  know,  all  salts  are  dissociated  more  than 
their  corresponding  acid,  and  so  the  red  color  due  to 
the  complex  ion  is  at  once  seen.  Ammonia  is  too 
weak  a  base  to  form  a  neutral  salt  in  very  dilute  solu- 
tions, and  so  the  results  obtained  in  its  presence  are 
not  sharp.  For  acids  this  indicator  is  very  good 

*  These  cases  have  been  taken  from  Ostwald's  book,  and  a 
large  mass  of  others  will  be  found  there,  to  which  I  would  refer 
the  reader. 


ANALYTICAL    CHEMISTRY.  63 

when  the  amount  of  free  acid  is  titrated  back  with  a 
solution  of  barium  hydroxide;  but  for  alkalies  it  is 
not  so  good,  as  it  is  restricted  to  the  very  strong  ones 
(i.e.,  those  that  are  largely  dissociated). 

Methylorange  is  a  medium  strong  acid  the  ion  of 
which  is  yellow,  the  undissociated  portion  being  red 
Addition  of  a  strong  acid  causes  the  hydrogen  ions  to 
go  back  into  the  undissociated  portion,  and  its  color 
(red)  appears.  If  it  is  mixed  with  a  base,  water  and 
a  salt  are  formed,  and  the  salt  being  dissociated  shows 
the  yellow  color.  If,  however,  to  methylorange  a 
weak  acid  is  added,  as  carbonic,  its  small  number  of  H 
ions  will  not  be  enough  to  drive  those  of  the  indicator 
back,  and  so  no  sharp  reaction  will  be  produced. 
Thus  methylorange  cannot  be  used  for  all  acids,  but 
only  for  the  stronger,  largely  dissociated,  ones.  For 
weak  bases  methylorange  is  the  better,  for  weak  acids 
phenolphthalein. 

Between  these  two  extremes  the  other  indicators 
lie,  and  their  actions  can  be  explained  in  the  same  way. 

We  have  now  finished  our  sketch  of  the  theory  of 
solution,  and  its  importance  can  be  appreciated. 
We  have  taken  up  only  the  more  important  parts;  but 
if  they  are  thoroughly  understood,  little  difficulty  will 
be  found  in  following  the  investigations  of  the  present 
day.  The  subject  is  becoming,  both  for  theoretical 
and  practical  chemistry  and  electricity,  more  and  more 
important  every  day,  and  I  feel  assured  that  by  going 
deeper  into  the  subject  and  reading  the  works  referred 
to  in  the  Preface  the  reader  will  find  both  pleasure 
and  profit, 


SHORT-TITLE   CATALOGUE 

OP  THE 

PUBLICATIONS 

OF 

JOHN   WILEY   &    SONS, 

NEW    YORK, 

LONDON:    CHAPMAN   &   HALL,  LIMITED. 
ARRANGED  UNDER  SUBJECTS. 


Descriptive  circulars  sent  on  application. 

Books  marked  with  an  asterisk  are  sold  at  net  prices  only. 

All  bcioks  are  bound  in  cloth  unless  otherwise  stated. 


AGRICULTURE. 

CATTLE  FEEDING — DISEASES  OF  ANIMALS— GARDENING,  ETC. 

Armsby's  Manual  of  Cattle  Feeding 12mo,  $1  75 

Downing's  Fruit  aud  Fruit  Trees 8vo,  5  00 

Kemp's  Landscape  Gardening. 12mo,  2  50 

Siockbridge's  Rocks  and  Soils 8vo,  2  50 

Lloyd's  Science  of  Agriculture 8vo,  4  00 

London's  Gardening  for  Ladies.     (Dow-ning.) 12mo,  1  50 

Steel's  Treatise  on  the  Diseases  of  the  Ox 8vo,  6  00 

"      Treatise  on  the  Diseases  of  the  Dog 8vo,  3  50 

Grotenfelt's  The  Principles  of  Modern  Dairy  Practice.     (Woll.) 

12mo,  2  00 
ARCHITECTURE. 
BUILDING — CARPENTRY— STAIRS,  ETC. 

Berg's  Buildings  and  Structures  of  American  Railroads 4to,  7  50 

Birkmire's  Architectural  Iron  and  Steel 8vo,  3  50 

"         Skeleton  Construction  in  Buildings 8vo,  3  00 

1 


Birkmire's  Compound  Riveted  Girders 8vo,  $2  00 

American  Theatres— Planning  and  Construction. 8vo,  3  00 

Carpenter's  Heating  and  Ventilating  of  Buildings 8vo,  3  00 

Freitag's  Architectural  Engineering 8vo,  2  50 

Kidder's  Architect  and  Builder's  Pocket-book Morocco  flap,  4  00 

Hatfield's  American  House  Carpenter 8vo,  5  00 

"        Transverse  Strains 8vo,  5  00 

Monckton's  Stair  Building — Wood,  Iron,  and  Stone 4to,  4  00 

Gerhard's  Sanitary  House  Inspection 16mo,  1  00 

Downing  and  Wightwick's  Hints  to  Architects 8vo,  2  00 

Cottages 8vo,  250 

Holly's  Carpenter  and  Joiner 18m<>.  75 

Worcester's  Small  Hospitals-  -Establishment  and  Maintenance, 
including  Atkinson's  Suggestions  for  Hospital  Archi- 
tecture   12mo,  125 

The  World's  Columbian  Exposition  of  1893 4to,  2  50 

ARMY,  NAVY,  Etc. 

MILITARY  ENGINEERING — ORDNANCE — PORT  CHARGES,  ETC. 

Cooke's  Naval  Ordnance 8vo,  $12  50 

Metcalfe's  Ordnance  and  Gunnery 12mo,  with  Atlas,  5  00 

Ingalls's  Handbook  of  Problems  in  Direct  Fire 8vo,  4  00 

Ballistic  Tables 8vo,  1  50 

Bucknill's  Submarine  Mines  and  Torpedoes 8vo,  4  00 

Todd  and  Whall's  Practical  Seamanship 8vo,  7  50 

Mahan's  Advanced  Guard 18mo,  1  50 

"      Permanent  Fortifications.  (Mercur.).8vo,  half  morocco,  7  50 

Wheeler's  Siege  Operations 8vo,  2  00 

Woodhull's  Notes  on  Military  Hygiene 12mo,  morocco,  2  50 

Dietz's  Soldier's  First  Aid 12mo,  morocco,  1  25 

Young's  Simple  Elements  of  Navigation..  12mo,  morocco  flaps,  2  50 

Reed's  Signal  Service 50 

Phelps's  Practical  Marine  Surveying 8vo,  2  50 

Very's  Navies  of  the  World 8vo,  half  morocco,  3  50 

Bourne's  Screw  Propellers 4to,  5  00 

2 


Hunter's  Port  Charges 8vo,  half  morocco,  $13  00 

*  Dredge's  Modem  French  Artillery 4to,  half  morocco,  20  00 

Record   of   the   Transportation    Exhibits    Building, 

World's  Columbian  Exposition  of  1893.. 4to,  half  morocco,  15  00 

Mercur's  Elements  of  the  Art  of  War 8vo,  4  00 

Attack  of  Fortified  Places 12mo,  2  00 

Chase's  Screw  Propellers 8vo,  3  00 

Wiuthrop's  Abridgment  of  Military  Law 12mo,  2  50 

De  Brack's  Cavalry  Outpost  Duties.     (Carr.) ISmo,  morocco,  2  00 

Cionkhite's  Gunnery  for  Non-com.  Officers 18mo,  morocco,  2  00 

Dyer's  Light  Artillery . . .- 12mo,  3  00 

Sharpe's  Subsisting  Armies 18mo,  1  25 

' '       18mo,  morocco,  1  50 

Powell's  Army  Officer's  Examiner 12mo,  4  00 

Hoff's  Naval  Tactics 8vo,  150 

Bruff 's  Ordnance  and  Gunnery 8vo,  6  00 

ASSAYING. 

SMELTING — ORE  DRESSING— ALLOYS,  ETC. 

Furman's  Practical  Assaying 8vo,  3  00 

Wilson's  Cyanide  Processes 12mo,  1  50 

Fletcher's  Quant.  Assaying  with  the  Blowpipe..  12rno,  morocco,  1  50 

Ricketts's  Assaying  and  Assay  Schemes 8vo,  3  00 

*  Mitchell's  Practical  Assaying.     (Crookes.) 8vo,  10  00 

Thurstou's  Alloys,  Brasses,  and  Bronzes 8vo,  2  50 

Kunhardt's  Ore  Dressing 8vo,  1  50 

O'Driscoll's  Treatment  of  Gold  Ores 8vo,  2  00 

ASTRONOMY. 

PRACTICAL,  THEORETICAL,  AND  DESCRIPTIVE. 

Michie  and  Harlow's  Practical  Astronomy 8vo,  3  00 

White's  Theoretical  and  Descriptive  Astronomy 12mo,  2  00 

Doolittle's  Practical  Astronomy Svo,  4  00 

Craig's  Azimuth 4to,  3  50 

Gore's  Elements  of  Geodesy 8vo,  2  50 

3 


BOTANY. 

GARDENING  FOR  LADIES,  ETC. 

Westermaier's  General  Botany.     (Schneider.) 8vo,  $2  00 

Thome's  Structural  Botany 18mo,  2  25 

Baldwin's  Orchids  of  New  England 8vo,  1  50 

London's  Gardening  for  Ladies.     (Downing.) 12mo,  1  50 

BRIDGES,  ROOFS,   Etc. 

CANTILEVER — HIGHWAY — SUSPENSION. 

Boiler's  Highway  Bridges 8vo,  2  00 

*  "       The  Thames  River  Bridge 4to,  paper,  500 

Burr's  Stresses  in  Bridges. 8vo,  3  50 

Merriman  &  Jacoby's  Text-book  of  Roofs  and  Bridges.     Part 

I.,  Stresses 8vo,  250 

Merriman  &  Jacoby's  Text-book  of  Roofs  and  Bridges.     Part 

II.,  Graphic  Statics 8vo.  2  50 

Merriman  &  Jacoby's  Text-book  of  Roofs  and  Bridges.     Part 

III.,  Bridge  Design 8vo,  5  00 

Merriman  &  Jacoby's  Text-book  of  Roofs  and  Bridges.     Part 

IV.,    Continuous,    Draw,    Cantilever,    Suspension, '  and 

Arched  Bridges (In  preparation). 

Crehore's  Mechanics  of  the  Girder 8vo,  5  00 

Du  Bois's  Strains  in  Framed  Structures 4to,  10  00 

Greene's  Roof  Trusses 8vo,  1  25 

Bridge  Trusses 8vo,  250 

"        Arches  in  Wood,  etc 8vo,  250 

Waddell's  Iron  Highway  Bridges 8vo,  4  00 

Wood's  Construction  of  Bridges  and  Roofs 8vo,  2  00 

Foster's  Wooden  Trestle  Bridges 4to,  5  00 

*  Morison's  The  Memphis  Bridge Oblong  4to,  10  00 

Johnson's  Modern  Framed  Structures 4to,  10  00 

CHEMISTRY- 

QUALITATIVE — QUANTITATIVE — ORGANIC — INORGANIC,  ETC. 

Fresenius's  Qualitative  Chemical  Analysis.    (Johnson.) 8vo,      4  00 

Quantitative  Chemical  Analysis.    (Allen.) 8vo,      6  00 

"  "  "  "  (Bolton.) 8vo,      1  50 

4 


Crafts's  Qualitative  Analysis.     (Schaeffer.) 12mo,  $1  50 

Perkins's  Qualitative  Analysis. 12mo,  1  00 

Thorpe's  Quantitative  Chemical  Analysis 18mo,  1  50 

Classen's  Analysis  by  Electrolysis.     (Herrick.) Svo,  3  00 

Stockbridge's  Rocks  and  Soils 8vo,  2  50 

O'Brine's  Laboratory  Guide  to  Chemical  Analysis Svo,  2  00 

Mixter's  Elementary  Text-book  of  Chemistry 12mo,  1  50 

Wulling's  Inorganic  Phar.  and  Med.  Chemistry 12mo,  2  00 

Mandel's  Bio-chemical  Laboratory .12mo,  1  50 

Austen's  Notes  for  Chemical  Students 12mo, 

Schimpf's  Volumetric  Analysis 12mo,  2  50 

Hammarsten's  Physiological  Chemistry  (Maudel.) 8vo,  .  4  00 

Miller's  Chemical  Physics 8vo,  2  00 

Pinner's  Organic  Chemistry.     (Austen.). 12mo,  1  50 

Kolbe's  Inorganic  Chemistry 12mo,  1  50 

Ricketts  and  Russell's  Notes  on  Inorganic  Chemistry  (Non- 
metallic)  Oblong  Svo,  morocco,  75 

DrechseFs  Chemical  Reactions.    (Merrill.) 12mo,  1  25 

Adriance's  Laboratory  Calculations 12mo,  1  25 

Troilius's  Chemistry  of  Iron '. 8vo,  2  00 

Allen's  Tables  for  Iron  Analysis Svo, 

Nichols's  Water  Supply  (Chemical  and  Sanitary) Svo,  2  50 

Mason's        "           "               "           "         "         Svo,  500. 

Spencer's  Sugar  Manufacturer's  Handbook .  12mo,  morocco  flaps,  2  00 

Wiechmanu's  Sugar  Analysis Svo,  2  50 

Chemical  Lecture  Notes 12mo,  300 

DRAWING. 

ELEMENTARY — GEOMETRICAL— TOPOGRAPHICAL. 
Hill's  Shades  and  Shadows  and  Perspective.  .  .  .(In  preparation) 

Mahan's  Industrial  Drawing.    (Thompson.) 2  vols.,  Svo,  3  50 

MacCord's  Kinematics Svo,  5  00 

Mechanical  Drawing Svo,  4  00 

"          Descriptive  Geometry Svo,  3  00 

Reed's  Topographical  Drawing.     (II.  A.) 4to,  5  00 

Smith's  Topographical  Drawing.     (Macmillan.) Svo,  2  50 

Warren's  Free-hand  Drawing    12nao,  1  00 

5 


Warren's  Drafting  Instruments 12mo,  $1  25 

"  Projection  Drawing 12rno,  150 

"  Linear  Perspective 12mo,  100 

Plane  Problems , 12mo,  125 

"  Primary  Geometry 12mo,  7."j 

"  Descriptive  Geometry 2  vols.,  8vo,  3  50 

"  Problems  and  Theorems 8vo,  .  2  50 

"  Machine  Construction 2  vols.,  8vo,  7  50 

"  Stereotomy — Stone  Cutting 8vo,  250 

"  Higher  Linear  Perspective 8vo,  3  50 

Shades  and  Shadows 8vo,  300 

Whelpley's  Letter  Engraving 12mo,  2  00 

ELECTRICITY  AND  MAGNETISM. 

ILLUMINATION— BATTERIES— PHYSICS. 

*  Dredge's  Electric  Illuminations 2  vols.,  4to,  half  morocco,  25  00 

Vol.  II 4to,  7  50 

Niaudet's  Electric  Batteries.     (Fishback. ) 12mo,  2  50 

Anthony  and  Brackett's  Text-book  of  Physics 8vo,  4  00 

Cosmic  Law  of  Thermal  Repulsion 18mo,  75 

Thurstou's  Stationary  Steam  Engines  for  Electric  Lighting  Pur- 
poses  12mo,  150 

Michie's  Wave  Motion  Relating  to  Sound  and  Light 8vo,  4  00 

Barker's  Deep-sea  Soundings 8vo,  2  00 

Holman's  Precision  of  Measurements 8vo,  2  00 

Tillman's  Heat 8vo,  1  50 

Gilbert's  De-nwgnete.     (Mottelay.) 8vo,  2  50 

Benjamin's  Voltaic  Cell 8vo,  3  00 

Reagan's  Steam  and  Electrical  Locomotives 12mo  2  00 

ENGINEERING. 

CIVIL — MECHANICAL— SANITARY,  ETC. 

*  Trautwine's  Cross-section Sheet,  25 

"            Civil  Engineer's  Pocket-book.  ..12mo,  mor.  Haps,  5  00 

*  "            Excavations  and  Embankments 8vo,  2  00 

*  "            Laying  Out  Curves 12mo,  morocco,  2  50 

Hudson's  Excavation  Tables.    Vol.  II 8vo,  1  00 

6 


Searles's  Field  Engineering 12mo,  morocco  flaps,  $3  00 

"       Railroad  Spiral 12nio,  morocco  flaps,  1  50 

Godwin's  Railroad  Engineer's  Field-book.  12mo,pocket-bk.  form,  2  50 

Butts's  Engineer's  Field-book 12mo,  morocco,  2  50 

Gore's  Elements  of  Goodesy 8vo,  2  50 

Wellington's  Location  of  Railways. 8vo,  5  00 

*  Dredge's  Perm.  Railroad  Construction,  etc.  . .  Folio,  half  mor.,  20  00 
Smith's  Cable  Tramways 4to,  2  50 

"      Wire  Manufacture  and  Uses 4to,  300 

Mahan's  Civil  Engineering.      (Wood.) 8vo,  5  00 

Wheeler's  Civil  Engineering 8vo,  4  00 

Mosely's  Mechanical  Engineering.     (Mahan.) 8vo,  5  00 

Johnson's  Theory  and  Practice  of  Surveying 8vo,  4  00 

Stadia  Reduction  Diagram.  .Sheet,  22£  X  28|  inches,  50 

*  Drinker's  Tunnelling 4to,  half  morocco,  25  00 

Eissler's  Explosives — Nitroglycerine  and  Dynamite 8vo,  4  00 

Foster's  Wooden  Trestle  Bridges 4to,  5  00 

Ruff ner's  Non-tidal  Rivers 8vo,  1  25 

Greene's  Roof  Trusses 8vo,  1  25 

"      Bridge  Trusses 8vo,  2  50 

' '  Arches  in  Wood,  etc 8vo,  2  50 

Church's  Mechanics  of  Engineering — Solids  and  Fluids 8vo,  6  00 

"  Notes  and  Examples  in  Mechanics 8vo,  200 

Howe's  Retaining  Walls  (New  Edition.) 12mo,  1  25 

Wegmann's  Construction  of  Masonry  Dams 4to,  5  00 

Thurston's  Materials  of  Construction. 8vo,  5  00 

Baker's  Masonry  Construction 8vo,  5  00 

"  Surveying  Instruments 12mo,  3  00 

Warren's  Stereotomy— Stone  Cutting 8vo,  2  50 

Nichols's  Water  Supply  (Chemical  and  Sanitary) 8vo,  2  50 

Mason's  "  "  "  "  "  8vo,  500 

Gerhard's  Sanitary  House  Inspection 16mo,  1  00 

Kirkwood's  Lead  Pipe  for  Service  Pipe 8vo,  1  50 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  00 

Howard's  Transition  Curve  Field-book 12mo,  morocco  flap,  1  50 

Craiida'iVs  The  Transition  Curve 12mo,  morocco,  1  50 

7 


Crandull's  Earthwork  Tables    8vo,  $1  50 

Pattern's  Civil  Engineering 8vo,  7  50 

"       Foundations 8vo,  5  00 

Carpenter's  Experimental  Engineering 8vo,  6  00 

Webb's  Engineering  Instruments 12mo,  morocco,  1  00 

Black's  U.  S.  Public  Works 4to,  5  00 

Merriman  and  Brook's  Handbook  for  Surveyors. . .  .12mo,  mor.,  2  00 

Merriman's  Retaining  Walls  and  Masonry  Dams 8vo,  2  00 

"          Geodetic  Surveying 8vo,  2  00 

Kiersted's  Sewage  Disposal 12rno,  1  25 

Siebert  and  Biggin's  Modern  Stone  Cutting  and  Masonry. .  .8vo,  1  50 

Kent's  Mechanical  Engineer's  Pocket-book 12mo,  morocco,  5  00 

HYDRAULICS. 

WATER-WHEELS — WINDMILLS — SERVICE  PIPE — DRAINAGE,  ETC. 

Weisbach's  Hydraulics.     (Du  Bois.) 8vo,  5  00 

Merriman's  Treatise  on  Hydraulics 8vo,  4  00 

Ganguillet&  Kutter'sFlow  of  Water.  (Hering&  Trautwine.).8vo,  4  00 

Nichols's  Water  Supply  (Chemical  and  Sanitary) 8vo,  2  50 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  a  00 

Ferrel's  Treatise  on  the  Winds,  Cyclones,  and  Tornadoes. .  .8vo,  4  00 

Kirkwood's  Lead  Pipe  for  Service  Pipe     8vo,  1  50 

Ruffner's  Improvement  for  Non-tidal  Rivers 8vo,  1  25 

Wilson's  Irrigation  Engineeriug 8vo.  4  00 

Bovey's  Treatise  on  Hydraulics, 8vo,  4  00 

Wegmann's  Water  Supply  of  the  City  of  New  York 4to,  10  00 

Hazen's  Filtration  of  Public  Water  Supply 8vo,  2  00 

Mason's  Water  Supply — Chemical  and  Sanitary 8vo,  5  00 

Wood's  Theory  of  Turbines 8vo.  2  50 

MANUFACTURES. 

ANILINE — BOILERS — EXPLOSIVES— IRON— SUGAR — WATCHES- 
WOOLLENS,  ETC. 

Metcalfe's  Cost  of  Manufactures 8vo,  5  00 

Metcalf's  Strd  (.Manual  for  Steel  Users) 12mo,  2  00 

Allen's  Tables  for  Iron  Analysis 8vo, 

8 


West's  American  Foundry  Practice 12mo,  $2  50 

"      Moulder's  Text-book  12mo,  250 

Spencer's  Sugar  Manufacturer's  Handbook 12mo,  inor.  flap,  2  00 

Wiechinaun's  Sugar  Analysis 8vo,  2  50 

Beaumont's  "Woollen  and  Worsted  Manufacture 12mo,  1  50 

*  Reisig's  Guide  to  Piece  Dyeing 8vo,  25  00 

Eissler's  Explosives,  Nitroglycerine  and  Dynamite 8vo,  4  00 

Reimann's  Aniline  Colors.     (Crookes.) 8vo,  2  50 

Ford's  Boiler  Making  for  Boiler  Makers 18mo,  1  00 

Thurston's  Manual  of  Steam  Boilers 8vo,  5  00 

Booth's  Clock  and  Watch  Maker's  Manual 12mo,  2  00 

Holly's  Saw  Filing 18mo,  75 

Svedelius's  Handbook  for  Charcoal  Burners 12mo,  1  50 

The  Lathe  and  Its  Uses .8vo,  600 

Woodbury's  Fire  Protection  of  Mills 8vo,  2  50 

Bolland'sThe  Iron  Founder 12mo,  2  50 

Supplement 12mo,  250 

"        Encyclopaedia  of  Founding  Terms 12mo,  3  00 

Bouvier's  Handbook  on  Oil  Painting 12mo,  2  00 

Steven's  House  Painting 18mo,  75 

MATERIALS  OF  ENGINEERING. 

STRENGTH — ELASTICITY — RESISTANCE,  ETC. 

Thurston's  Materials  of  Engineering 3  vols.,  8vo,  8  00 

Vol.  I.,  Non-metallic, 8vo,  200 

Vol.  II.,  Iron  and  Steel 8vo,  3  50 

Vol.  III.,  Alloys,  Brasses,  and  Bronzes 8vo,  2  50 

Thurston's  Materials  of  Construction 8vo,  5  00 

Baker's  Masonry  Construction • .  .8vo,  5  00 

Lanza's  Applied  Mechanics. 8vo,  7  50 

"        Strength  of  Wooden  Columns 8vo,  paper,  50 

Wood's  Resistance  of  Materials 8vo,  2  00 

Weyrauch's  Strength  of  Iron  and  Steel.    (Du  Bois.) 8vo,  1  50 

Burr's  Elasticity  and  Resistance  of  Materials 8vo,  5  00 

Merrirnan's  Mechanics  of  Materials 8vo,  4  00 

Church's  Mechanic's  of  Engineering — Solids  and  Fluids 8vo,  6  00 

9 


Beardslee  ami  Kent's  Strength  of  Wrought  Iron 8vo,  $1  50 

Hatfield's  Transverse  Strains 8vo,  5  00 

Du  Bois's  Strains  in  Framed  Structures 4to,  10  00 

Merrill's  Stones  for  Building  and  Decoration 8vo,  5  00 

Bovey's  Strength  of  Materials 8vo,  7  50 

Spalding's  Roads  and  Pavements 12mo,  2  00 

Rockwell's  Roads  and  Pavements  in  France '. 12mo,  1  25 

Byrne's  Highway  Construction 8vo,  5  00 

Pattou's  Treatise  on  Foundations 8vo,  5  00 

MATHEMATICS. 

CALCULUS — GEOMETRY — TRIGONOMETRY,  ETC. 

Rice  and  Johnson's  Differential  Calculus 8vo,  3  50 

Abridgment  of  Differential  Calculus 8vo,  1  50 

"  Differential  and  Integral  Calculus, 

2  vols.  in  1,  12mo,  2  50 

Johnson's  Integral  Calculus 12mo,  1  50 

Curve  Tracing 12mo,  1  00 

"        Differential  Equations— Ordinary  and  Partial 8vo,  350 

Least  Squares 12mo,  1  50 

Craig's  Linear  Differential  Equations 8vo,  5  00 

Merriman  and  Woodward's  Higher  Mathematics 8vo, 

Bass's  Differential  Calculus 12mo, 

Halsted's  Synthetic  Geometry 8vo,  1  50 

"       Elements  of  Geometry ...8vo,  175 

Chapman's  Theory  of  Equations .12mo,  1  50 

Merriman's  Method  of  Least  S  ;uures 8vo,  2  00 

Compton's  Logarithmic  Computations 12mo,  1  50 

Davis's  Introduction  to  the  Logic  of  Algebra 8vo,  1  50 

Warren's  Primary  Geometry 12mo,  75 

Plane  Problems 12mo,  125 

"        Descriptive  Geometry 2  vols.,  8vo,  3  50 

Problems  and  Theorems 8vo,  2  50 

"        Higher  Linear  Perspective 8vo,  3  50 

"         Free-hand  Drawing 12mo,  1  00 

"        Drafting  Instruments 12mo,  125 

10 


Warren's  Projection  Drawing * 12mo,  $1  50 

"        Linear  Perspective 12mo,  100 

"        Plane  Problems 12mo,  125 

Searles's  Elements  of  Geometry 8vo,  1  50 

Brigg's  Plane  Analytical  Geometry 12mo,  1  00 

Wood's  Co-ordinate  Geometry 8vo,  2  00 

Trigonometry 12mo,  100 

Mahan's  Descriptive  Geometry  (Stone  Cutting) 8vo,  1  50 

Woolf's  Descriptive  Geometry Royal  8vo,  3  00 

Ludlow's  Trigonometry  with  Tables.     (Bass.) 8vo,  300 

Logarithmic  and  Other  Tables.     (Bass.) 8vo,  2  00 

Baker's  Elliptic  Functions 8vo,  1  50 

Parker's  ^Quadrature  of  the  Circle 8vo,  2  50 

Totten's  Metrology 8vo,  2  50 

Ballard's  Pyramid  Problem 8vo,  1  50 

Barnard's  Pyramid  Problem 8vo,  1  50 

MECHANICS-MACHINERY. 

TEXT-BOOKS  AND  PRACTICAL  WORKS. 

Dana's  Elementary  Mechanics 12mo,  1  50 

Wood's          "                 "           12mo,  125 

"           Supplement  and  Key 1  25 

' '      Analytical  Mechanics 8vo,  3  00 

Michie's  Analytical  Mechanics 8vo,  4  00 

Merriman's  Mechanics  of  Materials Svo,  4  00 

Church's  Mechanics  of  Engineering Svo,  6  00 

"        Notes  and  Examples  in  Mechanics Svo,  2  00 

Mosely's  Mechanical  Engineering.     (Mahan.) Svo,  5  00 

Weisbach's    Mechanics    of   Engineering.     Vol.    III.,    Part  I., 

Sec.  I.     (Klein.) Svo,  500 

Weisbach's  Mechanics    of  Engineering.     Vol.   III.,    Part  I., 

Sec.  II.     (Klein.) Svo,  500 

Weisbach's  Hydraulics  and  Hydraulic  Motors.    (Du  Bois.)..8vo,  5  00 

Steam  Engines.     (Du  Bois.) , Svo,  500 

Lanza's  Applied  Mechanics Svo,  7  50 

11 


Crehore's  Mechanics  of  the  Girder » 8vo,  $5  00 

MacCord's  Kinematics 8vo,  5  00 

Thurston's  Friction  and  Lost  Work 8vo,  3  30 

"          The  Animal  as  a  Machine 12mo,  1  00 

Hall's  Car  Lubrication 12mo,  1  00 

Warren's  Machine  Construction 2  vols.,  8vo,  7  50 

Chordal's  Letters  to  Mechanics 12mo,  2  00 

The  Lathe  and  Its  Uses 8vo,  6  00 

Cromwell's  Toothed  Gearing 12mo,  1  50 

Belts  and  Pulleys -. . .  ,12mo,  150 

Du  Bois's  Mechanics.     Vol.  I.,  Kinematics 8vo,  3  50 

Vol.  II.,  Statics 8vo,  400 

Vol.  III.,  Kinetics 8vo,  350 

Dredge's     Trans.     Exhibits     Building,      World     Exposition, 

4to,  half  morocco,  15  00 

Flather's  Dynamometers 12mo,  200 

Rope  Driving 12mo,  200 

Richards's  Compressed  Air 12mo,  1  50 

Smith's  Press-working  of  Metals 8vo,  8  00 

Holly's  Saw  Filing 18uio,  75 

Fitzgerald's  Boston  Machinist 18mo,  100 

Baldwin's  Steam  Heating  for  Buildings .12mo,  2  50 

Metcalfe's  Cost  of  Manufactures 8vo,  5  00 

Benjamin's  Wrinkles  and  Recipes 12mo,  2  00 

Dingey's  Machinery  Pattern  Making 12mo,  2  00 

METALLURGY. 

IRON— GOLD— SILVER — ALLOYS,  ETC. 

Egleston's  Metallurgy  of  Silver 8vo,  7  50 

Gold  and  Mercury 8vo,  750 

"  Weights  and  Measures,  Tables ISnio,  75 

"  Catalogue  of  Minerals 8vo,  250 

O'Driscoll's  Treatment  of  Gold  Ores 8vo,  2  00 

*  Kerl's  Metallurgy— Copper  and  Iron 8vo,  15  00 

*  "           "               Steel,  Fuel,  etc 8vo,  1500 

12 


Tliurston's  Iron  and  Steel ^ 8vo,  $3  50 

Alloys 8vo,  2  50 

Troilius's  Chemistry  of  Iron Svo,  2  00 

Kunhardt's  Ore  Dressing  in  Europe Svo,  1  50 

Weyrauch's  Strength  of  Iron  and  Steel.     (Du  Bois.) Svo,  1  50 

Beardslee  and  Kent's  Strength  of  Wrought  Iron Svo,  1  50 

Comptou's  First  Lessons  in  Metal  Working 12mo,  1  50 

West's  American  Foundry  Practice 12mo,  2  50 

"      Moulder's  Text-book . .              12mo,  2  50 


MINERALOGY  AND  MINING. 

MINE  ACCIDENTS — VENTILATION— ORE  DRESSING,  ETC. 

Dana's  Descriptive  Mineralogy.     (E.  S.) Svo,  half  morocco,  12  50 

"      Mineralogy  and  Petrography.     (J.  D.) 12mo,  2  00 

"      Text-book  of  Mineralogy.    (E.  S.) Svo,  3  50 

"      Minerals  and  How  to  Study  Them.     (E.  S.) I2mo,  1  50 

"      American  Localities  of  Minerals Svo,  1  00 

Brush  and  Dana's  Determinative  Mineralogy Svo,  3  50 

Roseubusch's    Microscopical    Physiography  of    Minerals    and 

Rocks.     (Iddiugs.) Svo,  500 

Hussak's  Rock- forming  Minerals.     (Smith.) Svo,  2  00 

Williams's  Lithology Svo,  3  00 

Chester's  Catalogue  of  Minerals Svo,  1  25 

Dictionary  of  the  Names  of  Minerals Svo,  3  00 

Egleston's  Catalogue  of  Minerals  and  Synonyms Svo,  2  50 

Goodyear 's  Coal  Mines  of  the  Western  Coast 12mo,  2  50 

Kunhardt's  Ore  Dressing  in  Europe Svo,  1  50 

Sawyer's  Accidents  in  Mines Svo,  7  00 

Wilson's  Mine  Ventilation 16uio,  1  25 

Boyd's  Resources  of  South  Western  Virginia Svo,  3  00 

Map  of  South  Western  Virginia Pocket-book  form,  2  00 

Stockbridge's  Rocks  and  Soils Svo,  2  50 

Eissler's  Explosives — Nitroglycerine  and  Dynamite $vo,  4  00 

13 


^Drinker's  Tunnelling,  Explosives,  Compounds,  and  Rock  Drills. 

[4to,  half  morocco,  $25  00 

Beard's  Ventilation  of  Mines 12mo,  2  50 

Ihlseng's  Manual  of  Mining 8vo,  4  00 

STEAM  AND  ELECTRICAL  ENGINES,  BOILERS,  Etc. 

STATIONARY— MARINE— LOCOMOTIVE — GAS  ENGINES,  ETC. 

Weisbach's  Steam  Engine.     (Du  Bois.) 8vo,  500 

Thurston's  Engine  and  Boiler  Trials 8vo,  5  00 

"           Philosophy  of  the  Steam  Engine 12mo,  75 

"           Stationary  Steam  Engines 12mo,  1  50 

"           Boiler  Explosion 12mo,  150 

"  Steam-boiler  Construction  and  Operation 8vo, 

"          Reflection  on  the  Motive  Power  of  Heat.    (Carnot.) 

ISmo,  2  00 
Thurslon's  Manual  of  the  Steam  Engine.     Part  I.,  Structure 

and  Theory 8vo,  7  50 

Thurston's  Manual  of  the  Steam  Engine.     Part  II.,    Design, 

Construction,  and  Operation 8vo,  7  50 

2  parts,  12  00 

Rontgen's  Thermodynamics.     (Du  Bois. ) 8vo,  5  00 

Peabody's  Thermodynamics  of  the  Steam  Engine 8vo,  5  00 

Valve  Gears  for  the  Steam-Engine 8vo,  2  50 

Tables  of  Saturated  Steam Svo,  1  00 

Wood's  Thermodynamics,  Heat  Motors,  etc 8vo,  4  00 

Pupin  and  Osterberg's  Thermodynamics 12nio,  1  25 

Kncass's  Practice  and  Theory  of  the  Injector 8vo,  1  50 

Reagan's  Steam  and  Electrical  Locomotives 12mo,  2  00 

Meyer's  Modern  Locomotive  Construction 4to,  10  00 

Whitham's  Steam-engine  Design 8vo,  C  00 

"          Constructive  Steam  Engineering 8vo,  10  00 

Hemen way's  Indicator  Practice 12mo,  2  00 

Pray's  Twenty  Years  with  the  Indicator Royal  8vo,  2  50 

Spangler's  Valve  Gears 8vo,  2  50 

*  Maw's  Marine  Engines Folio,  half  morocco,  18  00 

Trow  bridge's  Stationary  Steatn  Engines 4to,  boards,  2  50 

14 


Ford's  Boiler  Making  for  Boiler  Makers 18mo,  $1  00 

Wilson's  Steam  Boilers.     (Flather. ) 12mo,  2  50 

Baldwin's  Steam  Heating  for  Buildings 12nio,  2  50 

Hoadley's  Warm-blast  Furnace 8vo,  1  50 

Sinclair's  Locomotive  Running 12mo,  2  00 

Clerk's  Gas  Engine , 12mo, 

TABLES,  WEIGHTS,  AND  MEASURES. 

Fou  ENGINEERS,  MECHANICS,  ACTUARIES— METRIC  TABLES,  ETC. 

Crandall's  Railway  and  Earthwork  Tables 8vo,  1  50 

Johnson's  Stadia  and  Earthwork  Tables 8vo,  1  25 

Bixby's  Graphical  Computing  Tables Sheet,  25 

Compton's  Logarithms 12mo,  1  50 

Ludlow's  Logarithmic  and  Other  Tables.     (Bass.) 12mo,  2  00 

Thurston's  Conversion  Tables 8vo,  1  00 

Egleston's  Weights  and  Measures 18mo,  75 

Tolteu's  Metrology 8vo,  2  50 

Fisher's  Table  of  Cubic  Yards Cardboard,  25 

Hudson's  Excavation  Tables.     Vol.  II 8vo,  1  00 

VENTILATION. 

STEAM  HEATING — HOUSE  INSPECTION — MINE  VENTILATION. 

Beard's  Ventilation  of  Mines 12mo,  2  50 

Baldwin's  Steam  Heating 12uio,  250 

Reid's  Ventilation  of  American  Dwellings 12mo,  1  50 

Mott's  The  Air  We  Breathe,  and  Ventilation 16nio,  1  00 

Gerhard's  Sanitary  House  Inspection Square  16rno,  1  00 

Wilson's  Mine  Ventilation 16mo,  1  25 

Carpenter's  Heating  and  Ventilating  of  Buildings 8vo,  3  00 

niSCELLANEOUS   PUBLICATIONS, 

Alcott's  Gems,  Sentiment,  Language Gilt  edges,  5  00 

Bailey's  The  New  Tale  of  a  Tub 8vo,  75 

Bal lard's  Solution  of  the  Pyramid  Problem 8vo,  1  50 

Barnard's  The  Metrological  System  of  the  Great  Pyramid.  .8vo,  1  50 

15 


*  Wiley's  Yosemite,  Alaska,  and  Yellowstone 4to,  $3  00 

Emmon's  Geological  Guide-book  of  the  Rocky  Mountains.  .8vo,  1  50 

Ferrel's  Treatise  on  the  Winds 8vo,  4  00 

Perkins's  Cornell  University Oblong  4to,  1  50 

Ricketts's  History  of  Rensselaer  Polytechnic  Institute 8vo,  3  00 

Mott's  The  Fallacy  of  the  Present  Theory  of  Sound . .  Sq.  IGmo,  1  00 
Rotherham's    The    New    Testament    Critically  Emphathized. 

12ino,  1  50 

Totteu's  An  Important  Question  in  Metrology 8vo,  2  50 

Whitehouse's  Lake  Moeris Paper,  25 

HEBREW  AND  CHALDEE  TEXT-BOOKS. 

FOR  SCHOOLS  AND  THEOLOGICAL  SEMINARIES. 

Gesenius's  Hebrew  and   Chaldee  Lexicon  to  Old   Testament. 

(Tregelles.) Small  4to,  half  morocco,  5  00 

Green's  Grammar  of  the  Hebrew  Language  (New  Edition ).8vo,  3  00 

"       Elementary  Hebrew  Grammar. 12mo,  1  25 

"       Hebrew  Chrestomathy 8vo,  2  00 

Letteris's    Hebrew  Bible  (Massoretic  Notes  in  English). 

8vo,  arabesque,  2  25 
Luzzato's  Grammar  of  the  Biblical  Chaldaic  Language  and  the 

Talmud  Babli  Idioms 12mo,  1  50 

MEDICAL. 

Bull's  Maternal  Management  in  Health  and  Disease 12mo,  1  00 

Mott's  Composition,  Digestibility,  and  Nutritive  Value  of  Food. 

Large  mounted  chart,  1  25 

Steel's  Treatise  on  the  Diseases  of  the  Ox 8vo,  6  00 

Treatise  on  the  Diseases  of  the  Dog 8vo,  3  50 

Worcester's  Small  Hospitals— Establishment  and  Maintenance, 
including  Atkinson's  Suggestions  for  Hospital  Archi- 
tecture  12mo,  1  25 

Hammarsten's  Physiological  Chemistry.   (Mandel.) 8vo,  4  00 


16      UNIVERSITY 


BOOK 


TO     - 


DAY 


AND 


FEB  19  1941 


'57BC 


Mi 


